Question

Write 2i in polar form.

Answer 1

Let, z = 2i

Let 0 = r cosθ and 2 = r sinθ

By squaring and adding, we get

(0)² + (2)² = (r cosθ)² + (r sinθ)²

⇒ 0+4 = r² (cos²θ + sin²θ)

⇒ 4 = r²

⇒ r = 2

∴ cosθ = 0 and sinθ = 1

Since, θ lies in first quadrant, we have

θ = π/2

Thus, the required polar form is \(2[cos(\frac{\pi}{2})+i\,sin(\frac{\pi}{2})]\)