SOLUTION: Use Euler's formula of e^(a + bi) = e^a(cos b + i sin b) to derive e^(πi) + 1 = 0. Please explain some of the steps in words.

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Question 1075784: Use Euler's formula of e^(a + bi) = e^a(cos b + i sin b) to derive e^(πi) + 1 = 0. Please explain some of the steps in words.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
e%5E%28a+%2B+bi%29+=+e%5Ea%28cos%28b%29+%2B+i%2Asin%28b%29%29

Just substitute a=0 and b=pi

e%5E%280+%2B+pi%2Ai%29+=+e%5E0%28cos%28pi%29+%2B+i%2Asin%28pi%29%29

e%5E%28pi%2Ai%29+=+1%28-1+%2B+i%2A%280%29%29

e%5E%28pi%2Ai%29+=+-1

e%5E%28pi%2Ai%29%2B1=0

Edwin