# Write the principal argument of (1 + i)2.

Let,

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

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

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