Question

What is the product of 16(cos(47)+isin(47)) and 4(cos(12)+isin(12))?

Answer 1

Write both complex numbers in polar form: (exp(x) is the same as e ˣ)

z = 16 (cos(47°) + i sin(47°)) = 16 exp(i 47°)

w = 4 (cos(12°) + i sin(12°)) = 4 exp(i 12°)

→ zw = 64 exp(i (47° + 12°)) = 64 exp(i 59°)

→ zw = 64 (cos(59°) + i sin(59°))