So, in uni with a few other students we had a seemingly paradox with complex numbers, but I think we solved it, wanted to share it with you guys anyways:
##i = e^{i\frac{\pi}{2}} = e^{\frac{1}{4}(2\pi i)} = (e^{2\pi i})^{\frac{1}{4}} = 1^{\frac{1}{4}} = 1##
On first and second glance this seems to be math-defying as ##i## is clearly not equal to ##1##. Below is the solution to this paradox we came up with.
So yeah, just thought it would be fun to share :P
I am nowhere near xedas math skills, please forgive me