So I'm reviewing some mathematics for quantum mechanics and this came equation came up(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\int_{-\infty}^{\infty} a \left( k \right)^{*} i \dfrac{d\,a\left(k\right)}{dk}dk[/itex].

If [itex]a \left( k \right)[/itex] is constrained to be real then this integral is zero or so the text says. Why is this the case? Is it because this is the summation of two orthogonal functions so the integral must be zero. If so how what would be the first steps to proving this to myself?

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# Integral of a real function multiplied by an imaginary function.

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