Question 5:

Convert the given complex number in polar form: – 1 – i

Answer

−1 – i

Let r cos θ = −1 and sin θ = −1

On squaring and adding, we obtain

r² cos² θ + r² sin² θ = (−1)² + (−1)²

⇒ r² (cos² θ + sin²⁺ θ) = 1 + 1

⇒ r² = 2

⇒ r = √2                        [Conventionally, r > 0]

∴ √2 cos θ = −1 and √2 sin θ = −1

This is the required polar form.

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