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in Complex Numbers by (50.7k points)
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Write the principal argument of (1 + i√3)2.

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Best answer

Let 0 = rcosθ and 2√3 = rsinθ

By squaring and adding, we get

(0)2 + (2√3)2 = (rcosθ)2 + (rsinθ)2

⇒ 0+(2√3)2 = r2 (cos2θ + sin2θ)

⇒(2√3)2 = r2

⇒ r = 2√3

∴ cosθ = 0 and sinθ = 1

Since, θ lies in first quadrant, we have

θ = π/2

Since, θ ∈ (-π ,π] it is principal argument.

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