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Name: Claire M.
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Question:
What is the logarithm of i?


Replies:
Clair,

Calculus can be used to prove that e^(ix) equals cos(x)+i*sin(x), if x is in radians. To make this function equal i, we set x equal to (pi)/2. The natural logarithm of e^(ix) is just i*x. Putting in our value for x, we find that ln(i)=i(pi/2).

Some will claim that this should work for x=5(pi)/2 as well. Since a logarithm is actually an inverse function, it is taken as defined only for

-(pi)


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