What is wrong with the reasoning in $(-1)^ \frac{2}{4} = \sqrt[4]{(-1)^2} = \sqrt[4]{1} = 1$ and $(-1)^ \frac{2}{4} = (-1)^ \frac{1}{2} = i$? $$(-1)^ \frac{2}{4} = \sqrt[4]{(-1)^2} = \sqrt[4]{1} = 1$$
$$(-1)^ \frac{2}{4} = (-1)^ \frac{1}{2} = i$$
Came across an interesting Y11 question that made pose this one to my self. I can't for the life of me, find the flaw in the initial reasoning.

We don't define rational power for negative numbers (accept odd roots, as user21820 noticed). Now, you can use branch cut (as user28120 noticed) to find root of $-1$ but if you do it so, you need to say that $(-1)^{1/2}=e^{ln(-1)\cdot1/2}$, and when you are doing it in this way, paradoxes won't appear.
