Let, z = -3i
Let 0 = r cosθ and -3 = r sinθ
By squaring and adding, we get
(0)2 + (-3)2 = (r cosθ)2 + (r sinθ)2
⇒ 0+9 = r2(cos2θ + sin2θ)
⇒ 9 = r2
⇒ r = 3
∴ cosθ = 0 and sinθ = -1
Since, θ lies in fourth quadrant, we have
θ = 3π/2
Thus, the required polar form is \(3[cos(3\frac{3\pi}{2})+i\,sin(\frac{3\pi}{2})]\)