1=1-1=1 ?

Algebra Level 5

I. Start with the famous identity eiπ=1e^{iπ}=-1.

II. So, eπ=(1)1/ie^π=(-1)^{1/i}.

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

IV. So, eπ/i=eiπe^{π/i}=e^{iπ}.

V. So, π/i=iππ/i=iπ or i2=1i^2=1.

VI. But i=1i=\sqrt{-1} or i2=1i^2=-1. So, 1=1-1=1.

In which step is there an error?

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