Question

Simplify : $\frac{(\cos \theta +i\sin \theta {)}^4}{(\cos \theta +i\sin \theta {)}^5}$

Answer 1

$\frac{(\cos \theta +i\sin \theta )4}{(\cos \theta +i\sin \theta )5}=\frac{1}{(\cos \theta +i\sin \theta )}$

$\Rightarrow \frac{1(\cos \theta -i\sin \theta )}{(\cos \theta +i\sin \theta )(\cos \theta -i\sin \theta )}$

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

$=\cos \theta -i\sin \theta$.