Hi

I'm having trouble with the problem below.

Let $\displaystyle z_1 = i$ and $\displaystyle z_2 = \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}i$

Plot $\displaystyle z_1 + z_2$ on an Argand diagram and deduce that $\displaystyle \tan\left(\frac{3\pi}{8}\right) = 1+\sqrt{2}$

I plotted them and the tangent of the resulting argument was indeed $\displaystyle 1+\sqrt{2}$, but I have no idea how to show that it is equal to $\displaystyle \frac{3\pi}{8}$. I've been staring blankly at it for an hour now, I know I'm going to kick myself when I see how it's done! :P

Stonehambey