Question

Convert the following in the polar form:

(i) , (ii)

Answer 1

(i) Here,

Let r cos θ = –1 and r sin θ = 1

On squaring and adding, we obtain

r² (cos² θ + sin² θ) = 1 + 1

⇒ r² (cos² θ + sin² θ) = 2
⇒ r² = 2 [cos² θ + sin² θ = 1]

∴z = r cos θ + i r sin θ

This is the required polar form.

(ii) Here,

Let r cos θ = –1 and r sin θ = 1

On squaring and adding, we obtain

r² (cos² θ + sin² θ) = 1 + 1
⇒r² (cos² θ + sin² θ) = 2

⇒ r² = 2 [cos² θ + sin² θ = 1]

∴z = r cos θ + i r sin θ

This is the required polar form.