# Problematic Proof?

Algebra Level 5
1. Any complex number $$z$$, with $$|z|=1$$ can be expressed in the form $$e^{i\theta +2ki\pi}$$.

2. $$(a^{b})^{c} = a^{bc}$$ meaning that $$z^{i}=e^{i*(i\theta +2ki\pi)} = e^{-\theta -2k\pi}$$

Result: $$z^{i}$$ holds an infinite number of values all with argument 0 but with a range of magnitudes.

Is there a problem with this and if so with which step does it lie?

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