Question

If $\left|Z\right|=2$ and $arg\left(Z\right)=\frac{\pi }{4}$ then write $Z$.

Answer 1

$Z=\left|Z\right|(\cos \theta +i\sin \theta )$

$=2(\cos \frac{\pi }{4}+i\sin \frac{\pi }{4})$

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

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