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.
2