- #1
diddy_kaufen
- 7
- 0
Homework Statement
Solve the equation
$$cos(\pi e^z) = 0$$
Homework Equations
I am not allowed to use the complex logarithm identities.
$$ \cos z = \frac{e^{iz}+e^{-iz}}{2} $$
$$e^{i\theta}=\cos\theta+i \sin\theta$$
The Attempt at a Solution
All I've gotten is $$\cos(\pi e^z)=0 \iff \pi e^z = \frac{\pi}{2}+p \pi \iff e^z=\frac{1}{2}+p, p\in Z $$
I have no idea how to solve this without resorting to the logarithm.