Answer
$-1-i$
Work Step by Step
$\sqrt 2$ cis $225^{\circ}$=$\sqrt 2(\cos225^{\circ}+i\sin225^{\circ})$
It is known that $\cos225^{\circ}=-\frac{\sqrt 2}{2}$ and $\sin135^{\circ}=-\frac{\sqrt 2}{2}$
Substituting these values in the expression and solving:
$\sqrt 2(\cos225^{\circ}+i\sin225^{\circ})=\sqrt 2(-\frac{\sqrt 2}{2}-\frac{\sqrt 2}{2}i)=(-\frac{\sqrt 2\times\sqrt 2}{2}-\frac{\sqrt 2\times\sqrt 2}{2}i)=(-\frac{2}{2}-\frac{2}{2}i)=-1-i$
