Question

Let z₁=r₁(cosθ₁+isinθ₁) and z₂=r₂(cosθ₂+isinθ₂) be complex numbers. z₁z₂=...?

a) r₁r₂(cos(θ₁+θ₂)+isin(θ₁+θ₂))
b) r₁r₂(cos(θ₁-θ₂)+isin(θ₁-θ₂))
c) r₁r₂(cosθ₁cosθ₂−sinθ₁sinθ₂+isinθ₁cosθ₂+cosθ₁sinθ₂)
d) r₁r₂(cosθ₁cosθ₂−sinθ₁sinθ₂+isinθ₁sinθ₂+cosθ₁cosθ₂)

Answer 1

The product of two complex numbers z1 and z2 is given by z1z2 = r1r2(cos(θ1+θ2)+isin(θ1+θ2)).

Step-by-step explanation:

The product of two complex numbers z1 and z2, represented in the form z1 = r1(cosθ1+isinθ1) and z2 = r2(cosθ2+isinθ2), is given by:

z1z2 = r1r2(cos(θ1+θ2)+isin(θ1+θ2))

Therefore, the correct option is a) r1r2(cos(θ1+θ2)+isin(θ1+θ2)).