Question 3:

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

Answer

1 – i

Let r cos θ = 1 and r sin θ = –1

On squaring and adding, we obtain

r² cos² θ + r² sin² θ = 1² + (−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

⇒ cos θ = 1/√2 and sin θ = −1/√2

∴ θ = −π/4            [As θ lies in the IV quadrant]

This is the required polar form.

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