Write z = (–1 + i√3) in polar form.

1.	Write z = (–1 + i√3) in polar form.
Answer» We have, z = (–1 + i√3) Let -1 = r cosθ and √3 = r sinθ By squaring and adding, we get (-1)² + (√3)² = (r cosθ)² + (r sinθ)² ⇒ 1+3 = r² (cos²θ + sin²θ) ⇒ 4 = r² ⇒ r = 2 ∴ cosθ = -1/2 and sinθ = √3/2 Since, θ lies in second quadrant, we have θ = π - π/3 = 2π/3 Thus, the required polar form is 2[cos\(\frac{2\pi}{3}\)+i sin\(\frac{2\pi}{3}\)]

Answer»

We have, z = (–1 + i√3)

Let -1 = r cosθ and √3 = r sinθ

By squaring and adding, we get

(-1)² + (√3)² = (r cosθ)² + (r sinθ)²

⇒ 1+3 = r² (cos²θ + sin²θ)

⇒ 4 = r²

⇒ r = 2

∴ cosθ = -1/2 and sinθ = √3/2

Since, θ lies in second quadrant, we have

θ = π - π/3 = 2π/3

Thus, the required polar form is 2[cos\(\frac{2\pi}{3}\)+i sin\(\frac{2\pi}{3}\)]

Discussion