Complex Numbers Vocabulary

A B C D E F I J L M N O P Q R S V

Concept

Definition

Example

absolute value

distance of a number from `0`

`| -4 | = 4`

acute angle

angle between `0°` and `90°`

`23^@`

alternating current (ac)

the back-and-forth movement of electrons in a wire

a common household voltage is `230\ "V"` ac

amperes (A)

unit for current

`57\ "A"`

angle

amount of turn

`143^@`

angular

to do with angles

angular velocity is a measure of the amount of turn per unit of time

application

a use for mathematics

ac circuits are one application of complex numbers

axis

line, part of graph

x-axis is usually the horizontal axis

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A B C D E F I J L M N O P Q R S V

Continues below

brackets

essential in mathematics

`(3 - 4j)(2 + 3j)`

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Concept

Definition

Example

capacitance

`Q / V` (charge/voltage). Units are farads.

`50\ "F"`

capacitive

To do with capacitance

-

capacitor (or condensor)

two conductors separated by an insulator - can store charge

-

circuit

A closed loop where current can flow

-

coefficient

the number multiplying a variable

`5` is the coefficient of `5x`

coil

wire wound around a cylinder

-

complex number

has a real part and an imaginary part

`5 + 2j`

`5` is the real part and `2` is the imaginary part

components

items that make up an electrical circuit

-

conjugate

a number involving radicals where the sign is changed

The conjugate of `5 + 7j` is `5 - 7j`

cube

raised to the power `3`

"x cubed" is x3

cubic

a polynomial of degree `3`

x3 + 5x2 + 3x - 2

current (A)

the flow of electrons in a circuit

-

cursor

the thing that follows the mouse position on a computer screen

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A B C D E F I J L M N O P Q R S V

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A B C D E F I J L M N O P Q R S V

degrees

unit for measuring angle

`251^@`

denominator

bottom part of a fraction

`4` is the denominator of `1/4`

digital

circuit which has only 2 outcomes: `0` or `1` (or "off" and "on")

...

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A B C D E F I J L M N O P Q R S V

Concept

Definition

Example

electromotive force (emf)

force that causes the motion of electrons due to voltage difference between two points

-

electron

particle of negative charge

-

engineer

someone whose idea of good interpersonal communication means getting the decimal point in the right place

safer not to say... :-)

exponential

growing (or decaying) according to an index relationship

the population of the world is growing at an exponential rate

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A B C D E F I J L M N O P Q R S V

farad

unit for capacitance

-

fractal

image created using iterations of complex numbers

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frequency

the rate of occurrence of a periodic wave

measured in hertz (`"Hz"`)

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A B C D E F I J L M N O P Q R S V

Concept

Definition

Example

imaginary number

a multiple of `j = sqrt(-1)`

`7j`

impedance (Z)

total opposition to the flow of current offered by a circuit

measured in ohms (`Ω`)

induced voltage

is generated in a conductor when subjected to a moving magnetic field

-

inductance

opposes a change in current

-

inductor

a conductor, usually wound into a coil to concentrate the magnetic lines of force and maximise the inductance

-

iteration

applying a number to a formula and applying the result to the formula again

I(n) = n2 + 3

I(1) = 12 + 3 = 4

I(4) = 42 + 1 = 17

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A B C D E F I J L M N O P Q R S V

j

square root of -1

j2 = −1

Julia

a common "set" in fractal images

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A B C D E F I J L M N O P Q R S V

Concept

Definition

Example

lags

time difference between 2 waveforms of the same frequency

voltage lags current by `0.1\ "s"`

leads

time difference between 2 waveforms of the same frequency

voltage leads current by `0.1\ "s"`

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A B C D E F I J L M N O P Q R S V

magnitude

size of a quantity like velocity or a complex number (does not include direction or angle)

the magnitude of `3 + 4j` is

`| 3 + 4j | = 5`

Mandelbrot

a common "set" in fractal images

-

modulus

same as "magnitude"

the modulus of `3 + 4j` is

`| 3 + 4j | = 5`

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A B C D E F I J L M N O P Q R S V

numerator

top part of a fraction

`3` is the numerator of `3/5`

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A B C D E F I J L M N O P Q R S V

ohms (W)

unit of resistance

a `50\ "kW"` resistor

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A B C D E F I J L M N O P Q R S V

Concept

Definition

Example

parallel

circuit having 2 or more paths for current flow

-

phase

time relationship between 2 waves

"voltage is in phase with current" means there is no lead or lag

pixel

a "picture element" or one dot of light on a computer monitor

an image which is `50 × 100` pixels

plates

part of a capacitor

-

polar coordinates

expressing a point in space in terms of its distance from a fixed point and its angle from a fixed line

`5\ ∠\ 35^@` means the point is `5` units from the origin and `35^@` from the horizontal positive axis

potential difference

a voltage difference between two points. Causes current to flow in a closed circuit

-

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A B C D E F I J L M N O P Q R S V

quadrant

one of 4 quarters of the x-y plane

the first quadrant is where both x and y are positive

quadratic

polynomial of degree 2

5x2 + 2x - 7 is quadratic

quotient

division

the quotient of `4` and `8` is `1/2`

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A B C D E F I J L M N O P Q R S V

Concept

Definition

Example

radians

alternative measure of angle

`pi` radians is `180^@`

rational number

can be written in the form p/q where p and q are integers

`7` is rational, so is `1/4`

π is irrational

rationalise (or rationalize)

to make rational

If the denominator of a fraction has `2 + sqrt(5)`, then part of the rationalising process is:

`(2 + sqrt5)(2 − sqrt5)`

`= 4 - 5 `

`= -1`

reactance (X)

Opposition to current flow without the dissipation of energy

effective resistance through a capacitor or inductor

real number

a number which does not involve imaginary numbers

`5, π, sqrt2` are real numbers

reciprocal of a number

1 divided by the number

the reciprocal of `2` is `1/2`

resistance

opposition to current flow

`5\ "W"`

resistor

material that opposes flow of current

-

roots

values of x (or other variable) that make an equation true.

the roots of the equation

2x2 + x - 1 = 0 are `x =1/2, -1`

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A B C D E F I J L M N O P Q R S V

series circuit

components are connected end to end

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A B C D E F I J L M N O P Q R S V

Concept

Definition

Example

vector

a quantity which has magnitude and direction

velocity, also acceleration. See the Vectors chapter.

voltage

electrical force that causes current to flow

-

voltmeter

for measuring voltage

-

volts (V)

unit for voltage

-

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A B C D E F I J L M N O P Q R S V

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