SOLUTION: Can somebody fill me in a bit on Euler’s formula? e^(a + bi) = e^a*(cos b + i sin b) -- Euler's Formula. His equation gives rise to e^(πi) + 1 = 0. '0, 1,π , e,

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Question 1075983: Can somebody fill me in a bit on Euler’s formula?
e^(a + bi) = e^a*(cos b + i sin b) -- Euler's Formula.
His equation gives rise to e^(πi) + 1 = 0.
'0, 1,π , e, and i' Are all in one equation.
Could you explain how Euler’s formula could be applied to derive this equation? Thank you very much.
Found 3 solutions by Edwin McCravy, Fombitz, math_helper:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Just substitute a=0 and b=p, 
like I told you before.  Also notice that in your post
you needed to put ^ to indicate exponents, not just
write them next to the base, for that shows multiplication
only, not exponentiation.  Also you must enclose the
exponents in parentheses.





Now we use the facts that , , and :





Add 1 to both sides:



Edwin
Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!

OK so when and ,
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!

Let a=0 so
Let so
Put the two together and the result is the famous Euler's Identity:

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