Question

Write z = (1 – i) in polar form.

Answer 1

We have, z = (1 – i)

Let 1 = r cosθ and -1 = r sinθ

By squaring and adding, we get

(1)² + (-1)² = (r cosθ)² + (r sinθ)²

⇒ 1+1 = r² (cos²θ + sin²θ)

⇒2 = r²

⇒ r = √2

∴ cosθ = 1/√2 and sinθ = -1/√2

Since, θ lies in fourth quadrant, we have

θ = -π/4

Thus, the required polar form is √2[cos\((-\frac{\pi}{4})\)+i sin\((-\frac{\pi}{4})\)]