Trigonometry Polar Complex

Question

What is the product (4V3 -4i)(V2 + VZi) in polar form? In what quadrant of the complex plane does the product lie?

Answer 1

Draw and label a diagram!

z₁ = 4√3 - 4i, ||z₁|| = 8, θ₁ = -π/6

z₂ = √2 - i√2, ||z₂|| = 2, θ₂ = π/4

z₁z₂ = ||z₁|| ||z₂|| [cos (θ₁ + θ₂) + i sin (θ₁ + θ₂)]