Complex Numbers In Polar Form: Demoivre's Theorem Question?

Question

In the following exercise, find the product of the complex number. Leave answer in polar form.

z1 = 1 + i
z2 = 2 + 2i

Answer 1

The x and y coefficients are equal in each case. That should let you quickly guess there's an angle of pi/4 involved in each case. (So the product will involve an angle of pi/2).

Given that hint, it should be pretty easy.

Answer 2

z1 * z2 = (1 + i)(2 + 2i) = 2 + 2i + 2i + 2i²

= 2 + 4i + 2(-1) = 2 + 4i - 2 = 4i