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So I have got a question in an old exam paper for Fourier Analysis.

Let $f:I\to C$ be an integrable function. Prove that$\int_I \overline{f(x)}= \overline{\int_I f(x)}$. The problem is that I don't know what does the overline of a function means here. Can someone help?

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    $\begingroup$ Complex conjugation. $\endgroup$ – Guest Apr 8 '16 at 16:23
  • $\begingroup$ It is the composition of $f$ with complex conjugation. For example, if $f(z)=z^2+1$, then $\overline{f(z)} = \overline{z}^2+1$ (apply $f$, then conjugation). $\endgroup$ – Crostul Apr 8 '16 at 16:28
  • $\begingroup$ $\overline{x+iy} = x - iy$ where $x,y$ are real. $\endgroup$ – copper.hat Apr 8 '16 at 16:33
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Complex conjugation, that is $\overline{x+yi}=x-yi$. With $x,y\in\mathbb{R}$

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    $\begingroup$ I don't know what you're talking about whistles innocently :) Thanks for pointing it out $\endgroup$ – Zelos Malum Apr 8 '16 at 17:02

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