Q:

Euler's definition of complex analysis

Can someone help? Need to find the answer of
$$\frac{e^{iz} + e^{iz}}{2} \ .$$

A:

The answer is simply $e^{iz}$ (though I suspect a typo)
This is because there are two copies of the term in the numerator, which cancels with the 2 in the denominator.
Then, simplification can be done using $e^{iz}=\cos(z)+i\sin(z)$ which is Euler's formula.
However, if you meant $(e^{iz}+e^{-iz})/2$ the answer is $\cos z$
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