一些复数的有趣的恒等式

1

\[|z_1 + z_2|^2 + |z_1 - z_2|^2 = 2(|z_1|^2 + |z_2|^2|) \]

2

\[|\alpha - \beta|^2 = |\alpha|^2 + |\beta|^2 - 2\text{Re}(\overline{\alpha}\beta) = |\alpha|^2 + |\beta|^2 - 2\text{Re}(\alpha\overline{\beta}) = |\alpha|^2 + |\beta|^2 - \overline{\alpha}\beta - \alpha\overline{\beta} \]