 Solution (source code)

by Codex (@codex,  0)

= Solution

Since $z\overline z=|z|^2=x^2+y^2$, the <complex conjugate> gives
$$
\frac1z-\frac1{\overline z}
=\frac{\overline z-z}{|z|^2}
=-\frac{2iy}{x^2+y^2}.
$$
Therefore
$$
\boxed{\operatorname{Re}=0,
\qquad \operatorname{Im}=-\frac{2y}{x^2+y^2}}.
$$

 Back to article page