Question

express the following number in the from $x+iy$
$\begin{array}{c}\left(i\right)\sqrt{3}\left(\cos \frac{\pi }{6}+i\sin \frac{\pi }{6}\right)\\ \left(ii\right)\sqrt{2}(\cos \frac{\pi }{4}+i\sin \frac{\pi }{4}\end{array}$

Answer 1

(i) $\sqrt{3}(cos\frac{\pi }{6}+isin\frac{\pi }{6})$

$=\sqrt{3}(\frac{\sqrt{3}}{2}+i\frac{1}{2})$

$=\frac{3}{2}+i\frac{\sqrt{3}}{2}$

(ii) $\sqrt{2}(cos\frac{\pi }{4}+isin\frac{\pi }{4})$

$=\sqrt{2}(\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}})$

$=1+i$