Question

Find the product of the complex numbers. Express your answer in trigonometric form.

Answer 1

In order to find the product of two complex numbers their magnitudes are multiplied and their arguments(measure of angles) are added up.

For z₁
Magnitude = 4
Argument = π/3

For z₂
Magnitude = 3
Argument = 2π/5

So, the product of z₁ and  z₂ will be:

$z_{1} z_{2} =4*3(cos( \frac{ \pi }{3}+\frac{2 \pi }{5})+isin( \frac{ \pi }{3}+\frac{2 \pi }{5})) \\ \\ z_{1} z_{2} =12(cos( \frac{11 \pi }{5}+isin( \frac{11 \pi }{5}))$