Find the product of the complex numbers. Leave the answer in polar form

Question

1.

2.

Answer 1

z₁z₂ = 16(cos(70° + 10°) + isin(70° + 10°)] = 16(cos80° + isin80°)

Answer 2

8(cos70+isin70) times 2(cos10+isin10) =

16(cos80 + isin80)

cos(A+B) = cosAcosB- sinAsinB

sin(A+B) = cosAsinB + sinAcosB

A=70, B =10

use FOIL

cos70+isin70 times cos10+isin10 =

cos70cos10 + isin70cos10 + isin10cos70 -sin10sin70 =

cos80+isin80

8x2 =16