Let, z = -2i

Let 0 = rcosθ and -2 = rsinθ

By squaring and adding, we get

(0)² + (-2)² = (rcosθ)² + (rsinθ)²

⇒ 0+4 = r²(cos²θ + sin²θ)

⇒4 = r²

⇒ r = 2

∴ cosθ= 0 and sinθ=-1

Since, θ lies in fourth quadrant, we have

Since, θ ∈ (-π ,π ] it is principal argument.