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Is it true that for every $z \in \mathbb{C}$

$$\begin{align} &2\mathfrak{Re}(\sinh z) &= \sinh z + \sinh \bar z\\ &2i\cdot \mathfrak{Im}(\sinh z) &= \sinh z - \sinh \bar z \end{align}$$

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Welcome to MSE, Michael. We will certainly help you - but to make it in a better way, could you tell what are the confusing points for you? E.g. would you put here how did you derive these formulas? –  Ilya Feb 20 '12 at 13:24
    
It was a step in a solution I was trying to follow. The question itself was about proving a function to be harmonic and finding it's conjugate. Thank you. –  Michael Feb 20 '12 at 14:05
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1 Answer

up vote 1 down vote accepted

This is true because the coefficients of the power series expansion of these entire functions are real.

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