hey im really dumb, but is $\displaystyle (e^{i \pi/4})^ 4 $ = $\displaystyle e^{i \pi} $ because $\displaystyle (e^{i \pi/4})^ 4 = e^{4 i \pi/4} $ ?
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Hello, Your computation is correct. And you are not dumb.
Congratulations. You have found a fourth root of -1 ($\displaystyle -1=e^{i\pi}$). How many others can you find?
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