Imaginary roots of negative numbers | Imaginary and complex numbers | Precalculus | Khan Academy
A1 A2 B1 B2 C1 C2
and
US / ənd /
•UK / ənd, ən,ænd /
- conjunction
- Used to refer to two or more things
- Plus; in addition; on top of that
- Used to introduce an action that follows another
complex
US / 'kɒmpleks /
•UK / kəmˈplɛks, ˈkɑmˌplɛks /
- adjecitve
- Not being simple; having many parts or aspects
- noun
- Group of buildings all used for the same purpose
- Psychological issue regarding self-image
only
US / ˈəunli /
•UK / ˈonli /
- 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
put
US / pʊt /
•UK / pʊt /
- phrasal verb
- to make a light stop shining by pressing or moving a switch
- verb
- To move or place a thing in a particular position
- To rate something in importance or value
- To write or say something in a certain manner
train
US / treɪn /
•UK / tren /
- noun
- Line of people, animals moving the same direction
- Vehicle that carries people and runs on rails
- Long rear section of a (e.g. wedding) dress
- Series of events happening one after another
- verb
- To teach a pet a behavior or a trick
- To educate someone in something, e.g. medicine
- To cause a plant to grow a certain way by cutting
- To point a certain way or toward something
- To practice to get better at a thing, e.g. sports
two
US / tu: /
•UK / tu /
- number
- 2
far
US / fɑ:(r) /
•UK / fɑr /
- adjecitve
- A long way away
- Being a long way away
- adverb
- To a large degree or extent
anything
US / ˈeniθɪŋ /
•UK / ˈɛniˌθɪŋ /
- pronoun
- A thing of any kind
invite
US / ɪnˈvaɪt /
•UK / ɪnˈvaɪt /
- noun
- An invitation
- verb
- To ask someone to go somewhere or do something
over
US / 'əʊvə(r) /
•UK / ˈovɚ /
- 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
any
US / 'enɪ /
•UK / ˈɛni /
- adjecitve
- One, or some, no matter which
- pronoun
- One (thing) of many; some
think
US / θɪŋk /
•UK / θɪŋk /
- verb
- To have an idea about something without certainty
- To have an idea, opinion or belief about something
then
US / ðen /
•UK / ðɛn /
- adverb
- A time that is not now
- Following another thing in time or arrangement
- Following on reasonably from what was just stated
- At that time, not now
right
US / raɪt /
•UK / raɪt /
- 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
each
US / i:tʃ /
•UK / itʃ /
- determiner
- Every one of two or more things
- pronoun
- Per one person or thing
example
US / ɪgˈzɑ:mpl /
•UK / ɪɡˈzæmpəl /
- noun
- Thing, person which represents a category
number
US / ˈnʌmbə(r) /
•UK / ˈnʌmbɚ /
- 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
US / skweə(r) /
•UK / skwɛr /
- 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
about
US / ə'baʊt /
•UK / əˈbaʊt /
- 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)
that
US / ðæt /
•UK / ðæt, ðət /
- 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
US / wɒt /
•UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /
- 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
sit
US / sɪt /
•UK / sɪt /
- verb
- To take an exam
- To be in a resting position on a chair
- To provide seating for people
- To remain in a still position while being painted
get
US / ɡet /
•UK / ɡɛt /
- 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
you
US / jʊ /
•UK / ju /
- pronoun
- Person someone is speaking or writing to
- Person or people in general
this
US / ðɪs /
•UK / ðɪs /
- 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
other
US / 'ʌðə(r) /
•UK / ˈʌðər /
- adjecitve
- A thing different from that mentioned
- determiner
- (Something) else; not the first (one)
- pronoun
- Being the one and only thing of that category
perfect
US / 'pɜ:fɪkt /
•UK / ˈpɚfɪkt /
- adjecitve
- So good it cannot be improved
- verb
- To do something so well, it cannot be done better
one
US / wʌn /
•UK / wʌn /
- 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
root
US / ru:t /
•UK / rut, rʊt /
- noun
- Emotional connection with a place, history etc.
- The origin or starting place of something
- A number that is multiplied by itself
- Part of plant growing underground, as to get water
- Part of tooth, hair etc. from which the rest grows
- Base part of a word to which affixes can be added
- verb
- To cause a plant to develop or grow roots
- (Animals) to search for e.g. food in earth
- To stop someone moving, as through fear
make
US / meɪk /
•UK / mek /
- 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
order
US / 'ɔ:də(r) /
•UK / ˈɔrdɚ /
- noun
- Religious or social group, as of nuns
- Instructions to others to do what you want
- State in which things are neat and organized
- What you ask to buy, e.g. food in restaurant
- Social or political control of an area
- verb
- To put things in a sequence, e.g. a, b, c
- To give instructions to others to do what you want
- To ask for something you want to buy, e.g. a meal
answer
US / 'ɑ:nsə(r) /
•UK / ˈænsɚ /
- noun
- Reply to a question someone asks
- Solution to a problem or test question
- verb
- To reply to a question someone asks
- To solve a test question or a problem
little
US / 'lɪtl /
•UK / ˈlɪtl /
- 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
US / let /
•UK / lɛt /
- verb
- To allow someone to do something
- Introducing a suggestion to do something together
- To rent a house, etc. to others
the
US / ðə /
•UK / ðə /
- 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
fact
US / fækt /
•UK / fækt /
- noun
- Something that is known or proved to be true
positive
US / ˈpɒzətɪv /
•UK / ˈpɑzɪtɪv /
- adjecitve
- Showing agreement or support for something
- Being sure about something; knowing the truth
- Having the charge produced by electrons
- Being good or useful
- Showing that a chemical is present in a test
ask
US / ɑ:sk /
•UK / æsk /
- verb
- To say to someone that you want something
since
US / sɪns /
•UK / sɪns /
- adverb
- At a point before the present time
- conjunction
- For this reason; because
- preposition
- From the time in the past that
well
US / wel /
•UK / wɛl /
- 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
just
US / dʒʌst /
•UK / dʒʌst /
- 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)
talk
US / tɔ:k /
•UK / tɔk /
- noun
- Style of speaking
- Discussion between two countries
- Giving information in front of people; lecture
- Saying things or ideas to someone with words
- verb
- To make a formal speech about something
- To say things or ideas to someone with words
for
US / fə(r) /
•UK / fɔr,fə /
- preposition
- Used to show the purpose, or need of something
time
US / taɪm /
•UK / taɪm /
- 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
why
US / waɪ /
•UK / hwaɪ, waɪ /
- adverb
- Question word to ask for a reason
- exclamation
- (Used to express surprise or approval)
branch
US / brɑ:ntʃ /
•UK / bræntʃ /
- noun
- Part of a family related to the same members
- Part of organization with a specific function
- Part of a tree growing outward from the trunk
- One of several streams combining to create a river
- Local office or store of a bank or large company
- (Often secret) group or subgroup of a religion
- Specific area of knowledge or study
- verb
- To separate away from the main part
definitely
US / ˈdefɪnətli /
•UK / ˈdefɪnətli /
- adverb
- Without question; beyond doubt
actually
US / ˈæktʃuəli /
•UK / ˈæktʃuəli /
- adverb
- Used to add new (often different) information
switch
US / swɪtʃ /
•UK / swɪtʃ /
- noun
- A change or shift from one method to another
- Thing you move to turn electrical items on or off
- Thin flexible piece of wood or stick
- verb
- To exchange or replace something for another thing
either
US / ˈaɪðə(r) /
•UK / ˈiðɚ, ˈaɪðɚ /
- adjecitve
- One of two (used when there is a choice of two)
- adverb
- (After negative statements) likewise, in addition
- conjunction
- Used as the first of two connected things
- determiner
- Used as the first of two connected things
- pronoun
- The one or the other
here
US / hɪə(r) /
•UK / hɪr /
- adverb
- In this place; at this location, position or time
inside
US / ˌɪn'saɪd /
•UK / ɪnˈsaɪd, ˈɪnˌsaɪd /
- adjecitve
- Being in something
- Being in a building
- adverb
- Into a house; indoors
- noun
- Inner part or surface of something
obviously
US / ˈɒbviəsli /
•UK / ˈɑːbviəsli /
- adverb
- In a way that is obvious/easy to see or understand
after
US / 'ɑ:ftə(r) /
•UK / ˈæftɚ /
- adverb
- Later than another time, or behind something
- conjunction
- Following something before
- preposition
- When an event happened or time has passed
continue
US / kən'tɪnju: /
•UK / kənˈtɪnju /
- verb
- To do something without stopping, or after pausing
- To start doing again after a break, pause, or stop
should
US / ʃʊd /
•UK / ʃʊd /
- other
- Used to indicate what is proper or reasonable
input
US / ˈɪnpʊt /
•UK / ˈɪnˌpʊt /
- noun
- Advice or ideas that someone provides
- verb
- To put in information, advice or opinions
reason
US / 'ri:zn /
•UK / ˈrizən /
- noun
- Ability to think about facts and form a judgment
- Explanation for why something occurred or was done
- verb
- To think and make conclusions in a logical manner
bit
US / bɪt /
•UK / bɪt /
- 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
multiply
US / ˈmʌltɪplaɪ /
•UK / ˈmʌltəˌplaɪ /
- verb
- To increase in number by reproducing/having babies
- To increase something by a large quantity
- To have increased by a large quantity
- To calculate two numbers e.g. 2 x 4
nonsensical
US / nɒnˈsensɪkl /
•UK / nɑnˈsɛnsɪkəl /
- adjecitve
- Making no sense; having no reason
rewrite
US / ˌri:'raɪt /
•UK / riˈraɪt /
- verb
- To write again to improve, or correct errors
work
US / wɜ:k /
•UK / wɚk /
- adjecitve
- Activity completed in order to make money
- noun
- The product of some artistic or literary endeavor
- Everything created by an author, artist, musician
- Activity you do in order to make money
- Place of employment
- Final product or result of a some labor or effort
- verb
- To bring into a specific state of success
- To be functioning properly, e.g. a car
- To do your job in your company or workplace
- To make an effort to do something
- To operate a machine or device
both
US / bəuθ /
•UK / boθ /
- determiner
- Used to refer to two things at the same time
- pronoun
- Used to refer to two things at the same time
result
US / rɪ'zʌlt /
•UK / rɪˈzʌlt /
- noun
- Something produced through tests or experiments
- Final score of a competition, election or game
- verb
- To be the outcome of other causes and effects
take
US / teɪk /
•UK / tek /
- 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
they
US / ðeɪ /
•UK / ðe /
- pronoun
- Two or more people, animals, or things
very
US / 'verɪ /
•UK / ˈvɛri /
- adjecitve
- Concerning a large degree or amount
- adverb
- A lot; much; many
- Used to stress or emphasize a noun
all
US / ɔ:l /
•UK / ɔl /
- adverb
- Completely; totally
- determiner
- Being every one of something
- pronoun
- 100% of something; the complete amount
its
US / ɪts /
•UK / ɪts /
- adjecitve
- Referring to or belonging to ‘it’
- determiner
- Of something; belonging or related to something
- other
- Possessive form of “it”
equal
US / 'i:kwəl /
•UK / ˈikwəl /
- adjecitve
- Same in shape, size, or number
- verb
- To add up or be the same as
now
US / naʊ /
•UK / naʊ /
- 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
reasoning
US / ˈri:zənɪŋ /
•UK / ˈrizənɪŋ /
- verb
- To think and make conclusions in a logical manner
principal
US / ˈprɪnsəpl /
•UK / ˈprɪnsəpəl /
- adjecitve
- Being the main or most important
- noun
- Leading person in a group of musicians or dancers
- Head teacher of a school
- Original amount of money borrowed
not
US / nɒt /
•UK / nɑt /
- adverb
- Word indicating the negative
- (Used to form the negative of verbs)
our
US / 'aʊə(r) /
•UK / aʊr /
- determiner
- Belonging to us
but
US / bət /
•UK / bʌt,bət /
- conjunction
- Used before you say something different, opposite
want
US / wɔnt /
•UK / wɑnt, wɔnt /
- noun
- Something you desire or wish for
- State or condition of poverty
- verb
- To desire or wish for something; hope for a thing
same
US / seɪm /
•UK / sem /
- adjecitve
- Being equal in quality and amount
- Identical; not different
- Not changing; constant
factorization
US / ˌfæktəraɪˈzeɪʃən /
•UK / ˌfæktərəˈzeɪʃən /
- noun
- Resolution of an entity into factors such that when multiplied together they give the original entit
can
US / kæn /
•UK / kən,kæn /
- noun
- A metal container for storing food
- other
- Able to; have the skill to; have the time to
- verb
- To have permission to
- To be possible to do
- To preserve food by sealing it in a metal container
imaginary
US / ɪ'mædʒɪnərɪ /
•UK / ɪˈmædʒəˌnɛri /
- adjecitve
- Not real; existing only in your imagination
with
US / wɪð /
•UK / wɪð, wɪθ /
- 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
have
US / həv /
•UK / hæv /
- 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
could
US / kəd /
•UK / kʊd /
- other
- Past form of 'can' to mean have ability
- Used to ask for something politely, or to offer
prime
US / praɪm /
•UK / praɪm /
- adjecitve
- Concerning the highest in quality or value
- Concerning the highest level of achievement
- Most important, chief importance in value
- verb
- To get a person ready for; prepare someone
- To coat with paint to prepare it for the main coat
negative
US / 'neɡətɪv /
•UK / ˈnɛɡətɪv /
- 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
radical
US / ˈrædɪkl /
•UK / ˈrædɪkəl,'rædɪkḷ /
- adjecitve
- Very new and different from what is traditional
- Concerning something's most basic part or form
- noun
- Person who believes in extreme political change
see
US / si: /
•UK / si /
- 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)
clear
US / klɪə(r) /
•UK / klɪr /
- 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