Answer
$\sqrt 2 + i \ \sqrt 2$
Work Step by Step
The given complex number can be written in the rectangular form as follows: $r (\cos \theta +i \sin \theta) = a+i b$
Where, $a=r \cos \theta ; b =r \sin \theta $
We are given that $r=2 $ and $\theta= 45^{\circ}$
Therefore, $2 (\cos 45^{\circ} +i \sin 45^{\circ}) = 2(\dfrac{\sqrt 2}{2}+ i \dfrac{\sqrt 2}{2}) \\ = \sqrt 2 + i \ \sqrt 2$
