Originally Posted by

**TomJerry** Express $\displaystyle z = \frac{(cos \theta + i sin \theta)^3(sin \theta + i cos \theta)}{(cos2 \theta - i sin2 \theta)}$ in the form $\displaystyle a+ib$

Solution :

$\displaystyle z = \frac{(cos \theta + i sin \theta)^3(sin \theta + i cos \theta)}{(cos2 \theta - i sin2 \theta)}$

$\displaystyle = \frac{(cos \theta + i sin \theta)^3(sin \theta + i cos \theta)}{(cos \theta + i sin \theta)^{-2}}$

$\displaystyle = (cos \theta + i sin \theta)^5(sin \theta + i cos \theta)$

**Stuck !!!!!**