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# Complex Numbers Vocabulary

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 240 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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 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

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capacitor (or condensor)

two conductors separated by an insulator - can store charge

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circuit

A closed loop where current can flow

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coefficient

the number multiplying a variable

5 is the coefficient of 5x

coil

wire wound around a cylinder

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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

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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

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cursor

the thing that follows the mouse position on a computer screen

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 degrees unit for measuring angle 251° denominator bottom part of a fraction 4 is the denominator of ¼ digital circuit which has only 2 outcomes - 0 or 1 (or "off" and "on") -

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Concept

Definition

Example

electro-motive force (emf)

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

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electron

particle of negative charge

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exponential

growing (or decaying) according to an index relationship

the population of the world is growing at an exponential rate

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 farad unit for capacitance - fractal image created using iterations of complex numbers - frequency the rate of occurrence of a periodic wave measured in hertz (Hz)

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Concept

Definition

Example

imaginary number

a multiple of j = √−1

7j

impedance (Z)

total opposition to the flow of current offered by a circuit

measured in ohms (W)

induced voltage

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

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inductance

opposes a change in current

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inductor

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

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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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 j square root of −1 j2 = −1 Julia a common "set" in fractal images -

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Concept

Definition

Example

lags

time difference between 2 waveforms of the same frequency

voltage lags current by 0.1 s

time difference between 2 waveforms of the same frequency

voltage leads current by 0.1 s

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 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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 numerator top part of a fraction 3 is the numerator of 3/5

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 ohms (W) unit of resistance a 50 kW resistor

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Concept

Definition

Example

parallel

circuit having 2 or more paths for current flow

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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

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polar coordinates

expressing a point in space in terms of its distance from a fixed point and its angle form 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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 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 ½.

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Concept

Definition

Example

alternative measure of angle

rational number

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

7 is rational, so is ¼

π is irrational

rationalise (or rationalize)

to make rational

If the denominator of a fraction has 2 + √5, then part of the rationalising process is:

(2 + √5) ×(2 − √5)
= 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, √2 are real numbers

reciprocal of a number

1 divided by the number

the reciprocal of 2 is ½

resistance

opposition to current flow

5 W

resistor

material that opposes flow of current

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roots

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

the roots of the equation

2x2 + x − 1 = 0 are x = ½, −1

 series circuit components are connected end to end -

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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

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voltmeter

for measuring voltage

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volts (V)

unit for voltage

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