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e, i, and π (Posted on 2004-03-02) Difficulty: 2 of 5
i = -1
e^(i π) = -1

(-e)^(i π) = ?

Simplify to a number without i. Leave e and π in their symbol forms.

See The Solution Submitted by Tristan    
Rating: 2.8571 (7 votes)

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Solution solution | Comment 1 of 12

(-e)^(iπ) = ((-1)e)^(iπ)
= (-1)^(iπ) * e^(iπ)
= (e^(iπ))^(iπ) * (-1)
= e^(i²π²) * (-1)
= e^(-π²) * (-1)
= - e^(-π²)


That comes out to about -0.0000517231862.
  Posted by Charlie on 2004-03-02 09:08:39
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