Complex Numbers Flashcards
1
Q
i
A
√-1
2
Q
General form of complex number
A
Z = x + iy
3
Q
Conjugate of a complex number
A
z̄ = x - iy
4
Q
z=z̄
A
If z is purely real
5
Q
z=-z̄
A
If z is purely imaginary
6
Q
Modulus of a complex number x+ iy
A
√(x²+y²)
7
Q
Product of complex number and its conjugate
A
zz̄ =|z|²
8
Q
Modulus amplitude form of complex number
A
Z = rcosθ + i rsinθ
OR
Z=re^iθ
r is the modulus of the complex number
9
Q
In modulus amplitude form
cosθ =
A
cosθ = x/r
OR
cosθ = x/√(x²+y²)
10
Q
In modulus amplitude form
sinθ =
A
sinθ = y/r
OR
sinθ = y/√(x²+y²)
11
Q
Which are the cube roots of unity?
A
1, w and w²
- w= (-1 +√3i) /2
- w² = (-1-√3i) /2
12
Q
properties of cube roots of unity
A
- 1+ w + w² = 0
- 1.w.w² = w³ =1
13
Q
for z= a + ib
Amplitude is?
A
tanθ= b/a
- Where θ is amplitude*
14
Q
z.z̅ =
A
z.z̅ = |z̅|²=|z|²
15
Q
For z = a + ib magnitude is?
A
√(a²+b²)
16
Q
If w is the nth root of unity then…
A
(1-w) (1+w²) (1-w³) …..(1-wⁿ⁺¹)=n
