Natural log of complex numbersDate: 8/31/96 at 12:28:13 From: Anonymous Subject: Natural log of complex numbers e^i*Pi=isin(Pi) + cos (Pi) = -1 If I square both sides: e^2i*Pi= 1 Taking the natural log, 2i*Pi=0 ! But how can the product of three constants = 0? Thanks in advance, David Date: 9/13/96 at 21:28:1 From: Doctor Ceeks Subject: Re: Natural log of complex numbers Hi, The natural logarithm is not well-defined on the complex plane for the same reason that the exponention function is not one to one. Thus, a=b does not imply ln(a)=ln(b). Your argument is similar to the following: 4 = 4. Take square roots. -2 = 2 ! -Doctor Ceeks, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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