Find the cartestian form of $6 - 7i$ rotated anticlockwise through $\frac{3\pi}{4}$ about the origin
I realize that I am going to be doing something like:
$\sqrt{85}e^{i\alpha}.e^{i\frac{3\pi}{4}}$ where $\alpha = \arctan{(\frac{7}{6})}$
and then converting to Cartesian form. I guess I am having trouble dealing with the $\alpha$ term since the answer I am trying to arrive at is $\frac{1 + 13i}{\sqrt{2}}$ , i.e, an exact representation not involving any $\arctan$ terms.
How do I arrive at the given answer?