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 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 |
A B C D E F I J L M N O P Q R S V
brackets |
essential in mathematics |
(3 − 4j)(2 + 3j) |
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 x^{3} |
cubic |
a polynomial of degree 3 |
x^{3} + 5x^{2} + 3x − 2 |
current (A) |
the flow of electrons in a circuit |
- |
cursor |
the thing that follows the mouse position on a computer screen |
- |
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 ¼ |
digital |
circuit which has only 2 outcomes - 0 or 1 (or "off" and "on") |
- |
A B C D E F I J L M N O P Q R S V
Concept |
Definition |
Example |
---|---|---|
electro-motive force (emf) |
force that causes the motion of electrons due to voltage difference between two points |
- |
electron |
particle of negative charge |
- |
exponential |
growing (or decaying) according to an index relationship |
the population of the world is growing at an exponential rate |
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 |
- |
frequency |
the rate of occurrence of a periodic wave |
measured in hertz (Hz) |
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 = √−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 |
- |
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) = n^{2} + 3 I(1) = 1^{2} + 3 = 4 I(4) = 4^{2} + 1 = 17 |
A B C D E F I J L M N O P Q R S V
j |
square root of −1 |
j^{2} = −1 |
Julia |
a common "set" in fractal images |
- |
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 |
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 |
numerator |
top part of a fraction |
3 is the numerator of 3/5 |
ohms (W) |
unit of resistance |
a 50 kW resistor |
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 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 |
- |
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 |
5x^{2} + 2x − 7 is quadratic |
quotient |
division |
the quotient of 4 and 8 is ½. |
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 |
p radians is 180° |
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) |
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 |
- |
roots |
values of x (or other variable) that make an equation true. |
the roots of the equation 2x^{2} + x − 1 = 0 are x = ½, −1 |
series circuit |
components are connected end to end |
- |
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 |
- |