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.