Complex Number Flashcards
1
Q
Complex number format
A
Z = real + imaginary no
Z = a + bi
2
Q
i = ?
A
i = √-1
3
Q
i^1 = ?
A
i^1 = i
4
Q
i^2 = ?
A
i^2= -1
5
Q
i^3= ?
A
i^3 = -i
6
Q
i^4 =?
A
i^4= 1
7
Q
(a+bi) . (a-bi) = ?
A
a^2+b^2
8
Q
Conjugate of z=a+bi
A
Z bar = a - bi
(change sign of number with i)
9
Q
Modulus of complex number
A
r = |z|= √ a^2 + b^2
10
Q
Amplitude/argument (θ)
A
θ = tan^-1(b/a)
11
Q
arg(z)
amp(z) = ?
mod(z)
A
θ, θ, r
12
Q
Cartesian form of complex number
A
z=a+bi
13
Q
Polar form of complex number
A
z=( r ,θ) on graph
z= r.(cosθ + i sinθ)
14
Q
Exponential form of complex number
A
z = r. e^iθ
15
Q
Power on complex number form
A
z^n= r. (cosθ + i sinθ) ^n
z^n= r. (cos n θ+ i sin n θ)
16
Q
w^3=?
A
1
17
Q
w^2=?
A
1/w
18
Q
w=?
A
w=1/w^2
19
Q
What is the complex cube root of unity
A
w
20
Q
w+1 =?
A
-w^2
21
Q
w^2+1=?
A
-w
22
Q
w^2+w=?
A
-1
23
Q
w^2+w+1=?
A
0
24
Q
Properties of modulus of complex number |z|
A
|z|=|z bar|=|-z|=|-z bar|=|zi|
25
z. z bar(conjugate)
|z|^2
26
|z^n|=?
|z|^n
27
|z1z2|=?
|z1||z2|
28
|z1 z2 z3... zn|=?
|z1||z2||z3|..... |zn|
29
|z1/z2|=?
|z1|/|z2| but z2 ≠0
30
Value of alpla and beta
Alpha = w
Beta = w^2
31
De moivre's theorem
•(cosθ+isinθ)^n=(cosnθ+isinnθ)
•(cosθ+isinθ)^-n=(cosnθ-isinnθ)
32
Square root of complex number formula trick
√a+bi=±(√|z|+a/2 + i √|z|-a/2)
33
Argument and magnitude meaning
Amplitude and modulus
