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Let $\{, \} : V \times V \rightarrow \mathbb{C}$ denote a Hermitian inner product on a vector space $V$ over the field of complex numbers $\mathbb{C}$.

Let $\langle,\rangle: V\times V\rightarrow \mathbb{R}$ denote the real part of $\{,\}$.

I want to show that $\{v,w\}=\langle v,w\rangle- i\langle iv,w\rangle$

Any hints.

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    $\begingroup$ Note the proper use of angle brackets, as in my edit to your question. $\endgroup$ Sep 3, 2017 at 20:33

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$$\Im \{v,w\} = \Re (-i \{v,w\}) = \langle -iv, w \rangle.$$

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