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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