Complex Numbers

Question 1

Modulus

Answer 1

|z| = √(x²+y²) = √(z*z^)

z^ = complex conjugate

Question 2

Complex Number

General Form

Answer 2

z = x + iy

Question 3

Complex Number

Polar Form

Answer 3

z = rcosθ = isinθ

Question 4

De Moivre’s Theorem

Answer 4

(r(cosθ+isinθ))^n =

r^n(cos(nθ)+isin(nθ))

Question 5

Complex Number Exponential Form

Answer 5

z = re^(iθ)

Question 6

Complex Roots

Answer 6

finding the nth root of a complex number yields n distinct solutions