Let be a non-real complex number lying on

MATHEMATICS · Subjective · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Let

z

be a non-real complex number lying on

|z| = 1

. Prove that

z = \frac{1+i \tan\left(\frac{\arg(z)}{2}\right)}{1-i \tan\left(\frac{\arg(z)}{2}\right)} \quad (\text{where } i = \sqrt{-1}).