Question 4:

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 = (−1)² + 1²

⇒ r²(cos² θ + sin² θ) = 1 + 1

⇒ r² = 2

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

∴√2 cos θ = −1 and √2 sin θ = 1

It can be written

This the required polar form .

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