express the following complex numbers in polar from.

Question

a. 1+√3i.
b. 3√3+3i.

Answer 1

r^2 = x^2+y^2
tanθ = y/x
so,
(a) r^2 = 1+3 = 4
tanθ = √3
so
1+√3i = 2cis(π/3)

(b) 3√3+3i = 6cis(π/6)