Question

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

The correct answer is 12(cos(11pi/15)+isin(11pi/15))

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( ( \pi )/(3)+(2 \pi )/(5))+isin( ( \pi )/(3)+(2 \pi )/(5))) \\ \\ z_(1) z_(2) =12(cos( (11 \pi )/(5)+isin( (11 \pi )/(5)))`