Question

Express the given number in the form x + iy.
$\sqrt{3}(\cos \frac{\pi}{6}+i\sin \frac{\pi}{6})$

Answer 1

To express the given number in the form x + iy.
$\sqrt{3}(\cos \frac{\pi}{6}+i\sin \frac{\pi}{6})$

put the value of
$\sin( \frac{\pi}{6} ) = \frac{1}{2} \\ \\ \cos( \frac{\pi}{6} ) = \frac{ \sqrt{3} }{2}$
$\sqrt{3}(\cos \frac{\pi}{6}+i\sin \frac{\pi}{6}) \\ \\ = \sqrt{3}( \frac{ \sqrt{3} }{2}+i \frac{1}{2}) \\ \\ x + iy= ( \frac{3}{2} + i \frac{ \sqrt{3} }{2} ) \\ \\ here \\ \\ x = \frac{3}{2} \\ \\ y = \frac{ \sqrt{3} }{2}$
Hope it helps you.