Complex Numbers

Question 1

How do you add complex numbers
If z = a + bj and w = c + dj

Answer 1

z + w = (a+c) + j(b+d)

Question 2

Multiplication of complex numbers:
If z = a + bj and w = c + dj

Answer 2

z.w = ac - bd + j(ad + cb)

Question 3

Division of complex numbers:
If z = a + bj and w = c + dj

Answer 3

a + jb c - jd
——— x ———
c + jd c - jd

Question 4

Find the complex conjugate of z = a + bj

Answer 4

z̄ = a - bj

Question 5

(cos(x) + j sin(x))^n = …

Answer 5

cos(nx) + j sin(nx)

Question 6

z.w = r(cos θ + j sin θ).s(cos γ + j sin γ)

Answer 6

= rs (cos (θ+ γ) + j sin (θ+ γ))

Question 7

express in z = a + jb polar form and exponential form

Answer 7

= r (cos θ +j sin θ) = re^jθ

Question 8

When expressing the complex number in polar form what do I change

Answer 8

cos x = cos (x + 2kπ)

Question 9

How many forms do you inspect

Answer 9

As many as the power of z is raised to ie z^3 = 3, always starting from k=0

Question 10

What does argument mean?

Answer 10

Angle, from positive x axis

Question 11

j^2 =

Answer 11

-1

Question 12

j^2 =

Answer 12

-1

Question 13

binomial theorem

Answer 13

(x + y)^n = a0 x^n + a1 x^n-1 y^1 + a2 x^n-2 y^2 + … + an y^n