I'm trying to understand the triangle inequality theorem and part of proof contains $$2\textrm{Re}(\left<a|b\right>) \leqq 2\left|\left<a|b\right>\right|.$$ Can someone show me how this is so?
2026-05-15 13:27:48.1778851668
Triangle Inequality Theorem
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The result of the inner product $\left<a|b\right>$ is a complex number, so let's write it as $c+id$. $$\textrm{Re}(c+id) = c$$ $$\left|c+id\right| = \sqrt{c^2 + d^2}$$