Euler's equation not making sense

[fractalzen]

Given: e^(i*pi) = -1 and e^(2*i*pi)=1

Adding we get: e^(i*pi) + e^(2*i*pi) = (-1+1) = 0

Factoring gives e^(i*pi) * [ 1 + e^(i*pi) ] = 0

so setting the second factor = to 0 gives 1 + e^(i*pi) = 0 which gives e^(i*pi)=-1

Okay so far, but setting the first factor = to 0 does not work.

e^(i*pi) = -1 It does not equal 0.

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So what am I missing here?

 

[fresh_42]

Why should it be zero? In $5 \cdot 0 = 0$ the first factor isn't zero either.

Edit: You might want to read this:
https://www.physicsforums.com/insights/things-can-go-wrong-complex-numbers/

 

[fractalzen]

Of course! Thanks for the response and the link.