If , where and , find the ordered pair of…

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

Problem

\left( \frac{3}{2} + \frac{i\sqrt{3}}{2} \right)^{50} = 3^{25}(x - iy)

, where

x, y \in \mathbb{R}

and

i = \sqrt{-1}

, find the ordered pair of

(x, y)