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A comment on Why is e^(pi i) = -1?. Parent comment
e^(ix) = cos(x) - i sin(x)
Since sin(π) == 0, i * 0 == 0 so you have cos(π) left which is -1.
So in sum:
e^(i π) = cos(π) - i sin(π) == -1 - 0 == -1
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e^(ix) = cos(x) - i sin(x)
Since sin(π) == 0, i * 0 == 0 so you have cos(π) left which is -1.
So in sum:
e^(i π) = cos(π) - i sin(π) == -1 - 0 == -1