Logarithm of i
Name: Claire M.
What is the logarithm of i?
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
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Update: June 2012