Question 6:

Convert the given complex number in polar form : −3

Answer

−3

Let r cos θ = −3 and r sin θ = 0

On squaring and adding, we obtain

r² cos² θ + r² sin² θ =(−3)²

⇒ r²(cos² θ + sin² θ) = 9

⇒ r² = 9

⇒ r = √9 = 3        [Conventionally, r >0]

∴ 3 cos θ = −3 and 3 sin θ = 0

⇒ cos θ = −1 and sin θ = 0

∴ θ = π

∴ −3 = r cos θ + i r sin θ = 3 cos π + B sin π = 3(cos π + i sin π)

This is the required polar form.

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