SOLUTION: Why does e<sup>i*pi</sup>+1=0 other than the fact that my calculator says so, and so I believe it?

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Question 431413: Why does ei*pi+1=0 other than the fact that my calculator says so, and so I believe it?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Apparently it seems like the other tutor taught you this...:)

From Euler's formula, e%5E%28i%2Atheta%29+=+cos%28theta%29+%2B+i%2Asin%28theta%29. By substituting theta+=+pi you will obtain e%5E%28i%2Api%29+=+-1, e%5E%28i%2Api%29+%2B+1+=+0. Euler's formula itself is derived using the Maclaurin series for e%5Ex, namely e%5Ex+=+sum%28%28x%5Ek%29%2Fk%21%2C+k=0%2C+infinity%29 (you will learn this sometime in calculus).