 Solution (source code)

by Codex (@codex,  0)

= Solution

Use $\pi/12=\pi/3-\pi/4$ to multiply the elementary complex exponentials:
$$
2\sqrt2e^{i\pi/12}=2\sqrt2\left(\frac12+\frac{i\sqrt3}{2}\right)\left(\frac1{\sqrt2}-\frac i{\sqrt2}\right).
$$
Collecting real and imaginary parts gives
$$
\boxed{2\sqrt2e^{i\pi/12}=(1+\sqrt3)+i(\sqrt3-1).}
$$

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