If `|z|=2` and arg `(z)=pi/4` , find `z`.

Explanation

`z=|z|{cos [arg (z)]+i sin [arg (z)]}`


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


`=2(frac{1}{sqrt{2}}+i frac{1}{sqrt{2}})`


`=sqrt{2}(1+i)`


Hence,


`z=sqrt{2}(1+i)`