Find the modulus and the argument, in radians in terms of $\pi$, of
$$z_1=\frac{1+i}{1-i}, z_2=\frac{\sqrt2}{1-i}, z_3=\left(\frac{1+i}{1-i}\right)^2$$
Plot $z_1, z_2$ and $z_1+z_2$ on an Argand diagram.
Deduce that $\tan \dfrac{3\pi}{8}=1+\sqrt2$
I found $|z_1|=|z_2|=|z_3|=1$ and $\arg z_1=\frac{\pi}{2}, \arg z_2=\frac{\pi}{4},\arg z_3=\pi$. I plotted the Argand diagram. I cannot see how this leads on to the final part of the question. Thanks in advance.