\(-1=1 \)?

Algebra Level 5

I. Start with the famous identity \(e^{iπ}=-1\).

II. So, \(e^π=(-1)^{1/i}\).

III. So, \(e^{π/i}=(-1)^{(1/i) \times (1/i)}=(-1)^{-1}=-1\).

IV. So, \(e^{π/i}=e^{iπ}\).

V. So, \(π/i=iπ\) or \(i^2=1\).

VI. But \(i=\sqrt{-1}\) or \(i^2=-1\). So, \(-1=1\).

In which step is there an error?

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