Subtitles section
Repeat sentence
Subtitles mode
Full screen
Previous
Next
x 1.0
Playback speed
More

Complex Numbers

Video vocabulary

other

Copy vocabulary

US / 'ʌðə(r) /

UK / ˈʌðər /

A1
  • adjecitve
  • A thing different from that mentioned
  • determiner
  • (Something) else; not the first (one)
  • pronoun
  • Being the one and only thing of that category

one

Copy vocabulary

US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

little

Copy vocabulary

US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

let

Copy vocabulary

US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

the

Copy vocabulary

US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

may

Copy vocabulary

US / meɪ /

UK / me /

A1
  • noun
  • 5th month of the year
  • other
  • Used to express a desire
  • Expresses permission, possibility or probability
  • Used to show that a thing could be true

this

Copy vocabulary

US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

make

Copy vocabulary

US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

follow

Copy vocabulary

US / ˈfɔləu /

UK / ˈfɑlo /

A1
  • verb
  • To come after someone; be guided by someone
  • To support someone, e.g. singer or comedian
  • To be the logical result of something
  • To happen after something else happens
  • To believe a set of values or a moral teacher
  • To understand something happening or being said

solution

Copy vocabulary

US / səˈlu:ʃn /

UK / səˈluʃən /

A2
  • noun
  • Mix of a liquid and a solid or a gas
  • Way to solve or deal with a problem

how

Copy vocabulary

US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

kind

Copy vocabulary

US / kaɪnd /

UK / kaɪnd /

A1
  • adjecitve
  • In a caring and helpful manner
  • friendly and considerate
  • noun
  • One type of thing

you

Copy vocabulary

US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

could

Copy vocabulary

US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

know

Copy vocabulary

US / nəʊ /

UK / noʊ /

A1
  • verb
  • To be familiar with a person or place, thing
  • To feel sure or be convinced about something
  • To discover or be aware of something
  • To be able to distinguish
  • To have knowledge of things

before

Copy vocabulary

US / bɪˈfɔ:(r) /

UK / bɪˈfɔr,-ˈfor /

A1
  • adverb
  • At a time earlier than the present; previously
  • conjunction
  • In advance of something happening
  • preposition
  • In front of someone or something

have

Copy vocabulary

US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

part

Copy vocabulary

US / pɑ:t /

UK / pɑ:rt /

A1
  • adjecitve
  • To some degree; half; not fully
  • noun
  • Division of a book
  • Ratio of something, e.g. 3 of gin, 1 of tonic
  • A line in a person's hair, made with a comb
  • Character an actor plays on stage, movie, or TV
  • Some, but not all of a specific thing
  • Role in causing something to happen
  • verb
  • To make a line in a person's hair, by using a comb
  • To move two things apart creating a space
  • To leave someone, or to break off a relationship

unit

Copy vocabulary

US / ˈju:nɪt /

UK / ˈjunɪt /

B2
  • noun
  • One apartment in a building
  • Group of people, e.g. soldiers, that work together
  • A chapter of a textbook
  • A standard of measurement of something
  • Single item made by a company

clear

Copy vocabulary

US / klɪə(r) /

UK / klɪr /

A1
  • adjecitve
  • Empty; without anything in it or on it
  • Being certain and without doubt
  • Being without any streaks, spots, or cracks
  • Easy to understand; well-explained; obvious
  • adverb
  • Completely; entirely; through the whole of
  • Away from; free from
  • verb
  • To recover from or remove a problem
  • To get rid of the entire contents of
  • To give permission for something to happen
  • To make a place or surface empty by removing
  • To prove that someone is not guilty or to blame

problem

Copy vocabulary

US / ˈprɒbləm /

UK / ˈprɑbləm /

A1
  • adjecitve
  • Causing trouble
  • noun
  • Something difficult to deal with or causes trouble
  • Question to show understanding of a math concept

review

Copy vocabulary

US / rɪˈvju: /

UK / rɪˈvju /

A2
  • noun
  • Examination of soldiers and supplies
  • Opinion, as in a paper, about movie, book, or play
  • Studying again to remind yourself about something
  • verb
  • To carefully look at the quality of something
  • To formally examine something in the military
  • To write an opinion about movie, book, or play
  • To study again to remind yourself about something

negative

Copy vocabulary

US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

see

Copy vocabulary

US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

with

Copy vocabulary

US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

just

Copy vocabulary

US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

well

Copy vocabulary

US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

special

Copy vocabulary

US / 'speʃl /

UK / ˈspɛʃəl /

A1
  • adjecitve
  • Being additional or extra
  • Different, better or greater than normal
  • noun
  • Heavily discounted sales item

for

Copy vocabulary

US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

why

Copy vocabulary

US / waɪ /

UK / hwaɪ, waɪ /

A1
  • adverb
  • Question word to ask for a reason
  • exclamation
  • (Used to express surprise or approval)

time

Copy vocabulary

US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

equation

Copy vocabulary

US / ɪˈkweɪʒn /

UK / ɪˈkweʒən, -ʃən /

B1
  • noun
  • Mathematical statement showing things to be equal
  • Complex set of different facts, ideas or issues

combination

Copy vocabulary

US / ˌkɒmbɪ'neɪʃn /

UK / ˌkɑmbəˈneʃən /

B1
  • noun
  • Series of letters or numbers needed to open a lock
  • Act or result of mixing things together

right

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

value

Copy vocabulary

US / 'vælju: /

UK / ˈvælju /

A1
  • noun
  • Importance you attach to something
  • Some information expressed as a number
  • Stated price of something; worth
  • verb
  • To place a high importance on something
  • To say how much money something is worth

get

Copy vocabulary

US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

down

Copy vocabulary

US / daʊn /

UK / daʊn /

A1
  • adjecitve
  • Being sad, sick, or unhappy
  • Not operating, working, or functioning as expected
  • adverb
  • In a sitting or lying position
  • Towards or on the ground, floor, or bottom
  • Written or copied onto a piece of paper or book
  • noun
  • A period of play in American Football
  • The soft, smooth hairs that cover a bird's body
  • preposition
  • Along something's path, course, or direction
  • Going from a higher position to a lower position
  • verb
  • To eat or drink very quickly and without stopping

case

Copy vocabulary

US / keɪs /

UK / kes /

A1
  • noun
  • Container used to carry things, e.g. clothes
  • Set of facts about a crime
  • Set of facts about an event
  • Example or instance of something
  • verb
  • To find out about a place, as in planning to steal

about

Copy vocabulary

US / ə'baʊt /

UK / əˈbaʊt /

A1
  • adverb
  • To be ready to; going to
  • Nearly; approximately; roughly
  • Near; next to; close to
  • In every direction; in the area of
  • preposition
  • Concerning or of (a topic)

like

Copy vocabulary

US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

that

Copy vocabulary

US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

what

Copy vocabulary

US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

bunch

Copy vocabulary

US / bʌntʃ /

UK / bʌntʃ /

B1
  • noun
  • A group of things of the same kind
  • verb
  • To group people or things closely together
  • (Cloth) to gather/be gathered together in folds

number

Copy vocabulary

US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

square

Copy vocabulary

US / skweə(r) /

UK / skwɛr /

A2
  • adjecitve
  • Being fair or honest
  • Multiply a number by itself e.g. 2x2 or 6x6
  • noun
  • Shape with 4 equal length sides and 4 equal angles
  • The result of multiplying Length by the width
  • Open public area in the middle of the town
  • verb
  • To make something balance or be equal
  • To multiply a number by itself, e.g. 2x2 or 6x8
  • To straighten the edge to form a four-sided shape

solve

Copy vocabulary

US / sɒlv /

UK / sɑ:lv /

A2
  • verb
  • To figure out a way to handle a difficult problem

straightforward

Copy vocabulary

US / ˌstreɪtˈfɔ:wəd /

UK / stretˈfɔrwəd /

B1
  • adjecitve
  • Easy to do or understand; not complicated

all

Copy vocabulary

US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

take

Copy vocabulary

US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

bit

Copy vocabulary

US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

look

Copy vocabulary

US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

they

Copy vocabulary

US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

very

Copy vocabulary

US / 'verɪ /

UK / ˈvɛri /

A1
  • adjecitve
  • Concerning a large degree or amount
  • adverb
  • A lot; much; many
  • Used to stress or emphasize a noun

their

Copy vocabulary

US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

useful

Copy vocabulary

US / ˈju:sfl /

UK / ˈjusfəl /

A1
  • adjecitve
  • That can help with a particular task

vanilla

Copy vocabulary

US / vəˈnɪlə /

UK / vəˈnɪlə /

B2
  • adjecitve
  • Having the taste of vanilla
  • noun
  • Taste from seed of vanilla plant, as in ice cream

plus

Copy vocabulary

US / plʌs /

UK / plʌs /

A2
  • noun
  • A benefit or advantage
  • preposition
  • In addition; add
  • In addition to; Indicates a number above
  • Having a value greater than zero

here

Copy vocabulary

US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

once

Copy vocabulary

US / wʌns /

UK / wʌns /

A1
  • adverb
  • One time; one instance
  • At a time in the past
  • conjunction
  • When; as soon as

actually

Copy vocabulary

US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

realize

Copy vocabulary

US / 'ri:əlaɪz /

UK / ˈriəˌlaɪz /

A1
  • verb
  • To become aware of or understand mentally

write

Copy vocabulary

US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

sort

Copy vocabulary

US / sɔ:t /

UK / sɔrt /

A1
  • noun
  • Group or class of similar things or people
  • verb
  • To organize things by putting them into groups
  • To deal with things in an organized way

already

Copy vocabulary

US / ɔ:lˈredi /

UK / ɔlˈrɛdi /

A1
  • adverb
  • Having happened or been done before this time

will

Copy vocabulary

US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

imaginary

Copy vocabulary

US / ɪ'mædʒɪnərɪ /

UK / ɪˈmædʒəˌnɛri /

A2
  • adjecitve
  • Not real; existing only in your imagination

scale

Copy vocabulary

US / skeɪl /

UK / skel /

A2
  • noun
  • Size, level, or amount when compared
  • Small hard plates that cover the body of fish
  • Device that is used to weigh a person or thing
  • Range of numbers from the lowest to the highest
  • Dimensions or size of something
  • verb
  • To change the size of but keep the proportions
  • To climb something large (e.g. a mountain)
  • To remove the scales of a fish

not

Copy vocabulary

US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

but

Copy vocabulary

US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

especially

Copy vocabulary

US / ɪˈspeʃəli /

UK / ɛˈspɛʃəli, ɪˈspɛʃ- /

A1
  • adverb
  • More than usual; extremely

plain

Copy vocabulary

US / pleɪn /

UK / plen /

A1
  • adjecitve
  • Obvious; clearly so, true
  • Very simple, ordinary; not decorated; not striped
  • noun
  • Wide open area of flat, dry land

zero

Copy vocabulary

US / ˈzɪərəʊ /

UK / ˈzɪroʊ /

A1
  • noun
  • Temperature when water turns to ice
  • number
  • Number 0
  • verb
  • To set a scale or other device to show 0

really

Copy vocabulary

US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

physics

Copy vocabulary

US / ˈfɪzɪks /

UK / ˈfɪzɪks /

A1
  • other
  • The study of heat, light, and energy on objects

same

Copy vocabulary

US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

wacky

Copy vocabulary

US / 'wækɪ /

UK / ˈwæki /

A1
  • adjecitve
  • Quite strange, but in a creative way

seven

Copy vocabulary

US / ˈsevn /

UK / ˈsɛvən /

A1
  • number
  • Number 7

definition

Copy vocabulary

US / ˌdefɪˈnɪʃn /

UK / ˌdɛfəˈnɪʃən /

A2
  • noun
  • Explanation of word's meaning, as in dictionaries
  • The sharpness of an image on a screen
  • Visual clearness in a photo or on a screen

equal

Copy vocabulary

US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

now

Copy vocabulary

US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

neat

Copy vocabulary

US / ni:t /

UK / nit /

A2
  • adjecitve
  • That you approve of; cool
  • (Of alcohol) not weakened with water or a mixer
  • Not messy; clean and orderly; simple and effective

rest

Copy vocabulary

US / rest /

UK / rɛst /

A1
  • noun
  • Time when one relaxes, sleeps, or is inactive
  • State in which there is a lack of motion
  • Part of something remaining after some was used
  • verb
  • To stop working or avoid activity to recover
  • (Of dead person) to lie in a grave
  • To lean, support or place something against
  • To not be tired because you had enough sleep

any

Copy vocabulary

US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

complex

Copy vocabulary

US / 'kɒmpleks /

UK / kəmˈplɛks, ˈkɑmˌplɛks /

A2
  • adjecitve
  • Not being simple; having many parts or aspects
  • noun
  • Group of buildings all used for the same purpose
  • Psychological issue regarding self-image

hey

Copy vocabulary

US / heɪ /

UK / he /

A1
  • exclamation
  • What you say when you want someone's attention

real

Copy vocabulary

US / rɪəl /

UK / ˈriəl, ril /

A1
  • adjecitve
  • Actually existing or happening, not imagined
  • Being important or special

only

Copy vocabulary

US / ˈəunli /

UK / ˈonli /

A1
  • adverb
  • Just one; just that amount or thing; not more than
  • Not very important or serious
  • Just that type of thing, person
  • Short time ago; not before a certain time
  • conjunction
  • Except; but

familiar

Copy vocabulary

US / fəˈmɪliə(r) /

UK / fəˈmɪljɚ /

A2
  • adjecitve
  • Well-known or easily recognized

variable

Copy vocabulary

US / ˈveəriəbl /

UK / ˈveriəbl /

A2
  • adjecitve
  • Having the ability to change or vary
  • noun
  • Mathematical quantity with several values

version

Copy vocabulary

US / ˈvə:ʃən /

UK / ˈvɚʒən, -ʃən /

A2
  • noun
  • Different way that someone interprets something
  • New or different form of something
  • An updated form of some software

over

Copy vocabulary

US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

call

Copy vocabulary

US / kɔ:l /

UK / kɔl /

A1
  • noun
  • A order or request for action
  • The sound an animal makes, often when in danger
  • A correct prediction, e.g. a decision in a game
  • A short visit to a place or person
  • A decision by a referee or umpire in a game
  • verb
  • To make a request or order for action
  • (Animal) to make sounds to warn of danger
  • To announce the date of an election
  • To make a judgment about something
  • To give someone or something a name
  • To guess in advance the result or outcome
  • To visit a place or person for a short time
  • To phone someone
  • To speak, announce or shout in a loud voice

where

Copy vocabulary

US / hwɛə /

UK / hwɛr, wɛr /

A1
  • conjunction
  • At or in the place which
  • In whatever place
  • pronoun
  • Word you use to ask the location of something

and

Copy vocabulary

US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

back

Copy vocabulary

US / bæk /

UK / bæk /

A1
  • adjecitve
  • Farthest from the front e.g. in a classroom
  • adverb
  • Have returned to a place you were before
  • noun
  • The part of a chair that the upper body leans upon
  • Location at the rear of something
  • The reverse of side something
  • Area on the rear of your body
  • verb
  • To bet money on something
  • To go backwards in a car
  • To support and encourage someone or some cause

hopefully

Copy vocabulary

US / ˈhəʊpfəli /

UK / ˈhopfəli /

A2
  • adverb
  • In a manner wishing something to happen

lot

Copy vocabulary

US / lɒt /

UK / lɑt /

A1
  • noun
  • What happens to a person in life from chance; fate
  • A group of people seen together
  • Item for sale at an auction
  • Small area of land used for a purpose e.g. parking
  • Subtitles section
  • Write the following numbers as complex numbers.
  • And just as a little bit of review, a complex number is a number that has a real part or an imaginary part, or actually let me make that clear, has a real part and an imaginary part.
  • So if I, I'm gonna write some variables here, a plus bi, where a is real and b is real, this is a complex number.
  • This part right over here is the real part.
  • That is the real part of the number.
  • And this part right over here is imaginary.
  • And why is it imaginary?
  • Because it is a scaled up version of this special number, the imaginary unit.
  • It's the special number i.
  • It's scaled up by b in this case.
  • And you may or may not already be familiar, I know it's kind of a wacky thing, but the definition of i says that i squared is equal to negative one.
  • Hey, we didn't have any numbers before where if we took the square, we get negative one.
  • Now if you take i squared, you get negative one.
  • So what's neat about imaginary numbers is that their squares are negative.
  • And what's useful about them is it allows us to solve a bunch of equations that we couldn't have solved if you're only looking for real solutions.
  • It has all sorts of implications in engineering especially, and other things like physics and all the rest.
  • So right now, you just really have to go with this definition.
  • You just have to go with this definition in this one.
  • And as we do more numbers, and especially once you see a lot more engineering applications, hopefully you'll realize the value of i or the value of imaginary numbers.
  • So going back to the problem, write the following numbers as complex.
  • So this number right here, this is just a plain vanilla negative 21. It just looks like a real number to me.
  • Well, how do I write it as a complex number?
  • Well, I write it as a combination of a real and an imaginary number.
  • So I could just write this as negative 21, that's the real part, plus zero times i.
  • Zero times i is zero, so it's still just going to be negative 21. We have no imaginary part really.
  • So this is just the complex version of it.
  • Very straightforward.
  • Same thing down here.
  • Seven i is an imaginary number.
  • There's no real part to this.
  • So we could call this, the real part here is just zero.
  • So this is zero plus zero plus seven i.