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<Moderator's note: Moved from a homework forum.>

Given 0 < a < 1, i = √(-1),

e

but also, e

How to resolve the apparent contradiction?

e

e

No clue! This is embarrassing!

1. The problem statement, all variables and given/known data1. The problem statement, all variables and given/known data

Given 0 < a < 1, i = √(-1),

e

^{i2πa}= cos 2πa + i sin 2πabut also, e

^{i2πa}= (e^{i2π})^{a}= 1^{a}= 1How to resolve the apparent contradiction?

**2. Relevant equations**e

^{ab}= (e^{a)b}e

^{ix}= cos x + i sin x**3. The attempt at a solution**No clue! This is embarrassing!

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