# If $\;|z|=2\;$ and $\;arg(z) = \large\frac{\pi}{4}\;$ , then $\;z=$

$(a)\;\sqrt{3}(1+i)\qquad(b)\;\sqrt{2}(1+i)\qquad(c)\;1+i\qquad(d)\;\sqrt{5}(2+i)$

Answer : $\;\sqrt{2}(1+i)$
Explanation :
$z=|z| (cos \large\frac{\pi}{4} + i sin\large\frac{\pi}{4})$
$= 2 (\large\frac{1}{\sqrt{2}} +i \large\frac{1}{\sqrt{2}} )$
$=\sqrt{2}(1+i)\;.$