Question 7:

Convert the given complex number in polar form: √3 + i

Answer

√3 + i

Let r cos θ =√3 and r sin θ = 1

On squaring and adding, we obtain

r² cos² θ + r² sin² θ = (√3)² + 1²

⇒ r²(cos² θ + sin² θ) = 3 + 1

⇒ r² = 4

⇒ r = √4 = 2                     [Conventionally, r > 0]

∴ 2 cos θ = √3and 2 sin θ = 1

⇒ cos θ = √3/2 and sin θ = 1/2

∴ θ = π/6                 [As θ lies in the I quadrant]

This is the required polar form.

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