Answer
$-\sqrt 2-i\sqrt 2$
Work Step by Step
We know that $\cos225^{\circ}=-\frac{\sqrt 2}{2}$ and $\sin225^{\circ}=-\frac{\sqrt 2}{2}$
Substituting these values in the expression and solving:
$2(\cos225^{\circ}+i\sin225^{\circ})=2(-\frac{\sqrt 2}{2}-\frac{\sqrt 2}{2}i)=-\sqrt 2-i\sqrt 2$
Therefore, the rectangular form is $-\sqrt 2-i\sqrt 2$.
