15 questions linked to/from Does $i^4$ equal $1?$
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### What is wrong with this fake proof $e^i = 1$?

$$e^{i} = e^{i2\pi/2\pi} = (e^{2\pi i})^{1/(2\pi)} = 1^{1/(2\pi )} = 1$$ Obviously, one of my algebraic manipulations is not valid.
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### Exponent of a number is a square root?

Say you have a number $x^{\sqrt 2}$. Is there any way to represent this number so that there's no root (or irrational) as the exponent (so that it's easier to understand for me)? I just can't wrap my ...
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### Simple Complex Number Problem: $1 = -1$ [duplicate]

Possible Duplicate: -1 is not 1, so where is the mistake? I'm trying to understand the exact point of failure in the following reasoning: \begin{equation*} 1 = \sqrt{1} = \sqrt{(-1)(-1)} = \sqrt{...
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### What are multiplicative inverses?

Why does $i^{-4} = -1$? This arrises from the accepted answer of is $i^4$ equal to $-1$? In which the answerer states: The powers of $i$ are cyclic ... the pattern persists for negative ...
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### Why are the graph of $f(x) = (x^2)^\frac{1}{6}$ and the graph of $f(x) = x^\frac{1}{3}$ not the same?

Why is the graph of $f(x) = (x^2)^\frac{1}{6}$ not the same graph as $f(x) = x^\frac{1}{3}$? Shouldn't they be the same because when you apply the exponent rules to the first equation, you get the ...
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