 Solution (source code)

by Codex (@codex,  0)

= Solution

The two factors have <moduli> $\sqrt2$ and $2$, and <complex arguments> $\pi/4$ and $\pi/6$. Multiplication multiplies the <moduli> and adds the <complex arguments>, giving
$$
\boxed{|z|=2\sqrt2,\qquad\arg z=\frac{5\pi}{12}\pmod{2\pi}.}
$$
The displayed angle is the <principal argument> in radians; equivalently the argument is $75^\circ$ modulo $360^\circ$.

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