Explanation

Multiplication:
z₁z₂ = r₁r₂ [cos(θ₁ + θ₂) + i sin(θ₁ + θ₂)]

Division:
z₁/z₂ = (r₁/r₂) [cos(θ₁ − θ₂) + i sin(θ₁ − θ₂)]

This avoids messy algebra.

Quiz

1. What happens to r when dividing?

2. What happens to θ when dividing?

3. Is polar form efficient?

4. Is subtraction used in division?

5. Does this use trig identities?

Answer Key

1. r₁/r₂

2. θ₁ − θ₂

3. Yes

4. Yes

5. Yes