Answer
$$ - \sqrt 2 - \sqrt 2 i$$
Work Step by Step
$$\eqalign{
& {\text{Trigonometric form }}2\left( {\cos 225^\circ + i\sin 225^\circ } \right) \cr
& {\text{Calculate }}\cos 225^\circ {\text{ and }}\sin 225^\circ \cr
& \cos 225^\circ = - \frac{{\sqrt 2 }}{2} \cr
& \sin 225^\circ = - \frac{{\sqrt 2 }}{2} \cr
& {\text{,then}} \cr
& 2\left( {\cos 225^\circ + i\sin 225^\circ } \right) = 2\left( { - \frac{{\sqrt 2 }}{2} - \frac{{\sqrt 2 }}{2}i} \right) \cr
& = - \sqrt 2 - \sqrt 2 i \cr} $$
