Given that a complex number Z. = 1 + cos 2@ + isin 2@. Calculate its argument

Answer 1

z = 1+cos2θ + i sin2θ
we want z = r(cosØ+i sinØ), where

cosØ = 1+cos2θ
sinØ = sin2θ

That means that

(1+cos2θ)^2 + sin^2(2θ) = 1
2 + 2cos2θ = 1
cos2θ = -1/2

cosØ = 1 - 1/2 = 1/2
sinØ = √3/2
Ø = π/3