Modulus Identities

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  • $$|z_1 + z_2|^2 = |z_1|^2 + |z_2|^2 + 2 \mathrm{Re}(z_1 \bar{z_2})$$
  • $$|z_1 - z_2|^2 = |z_1|^2 + |z_2|^2 - 2 \mathrm{Re}(z_1 \bar{z_2})$$
  • $$|z_1 + z_2|^2 + |z_1 - z_2|^2 = 2(|z_1|^2 + |z_2|^2)$$
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