TITLE: What's wrong in this equation? (Regarding Euler's eqn)
QUESTION [5 upvotes]: I got an idea, but that doesn't match with Euler's theory.. So What's wrong?!
$$e^{jx} = (e^{j 2\pi})^{x/2\pi} = 1^{x/2\pi} = 1$$

REPLY [5 votes]: Raising a complex number of the form $e^{it}$ to another number $s$, where $s$ is not an integer is a multivalued function. Hence, your first step, i.e., $(e^{i 2\pi})^{x/2\pi} = e^{ix}$ is incorrect.