A Conversation for The Euler Equation
dysprosia Started conversation Feb 9, 2002
Ln of negative numbers is multiple valued:
bobdylan_mcfc Posted Jul 24, 2009
Yes, but in fact this is true of any number. Since e^(2.pi.i) = 1, we can add 2.pi.i to any log. In fact you can't define the logarithm as a continuous function from the complex plane without zero* to the complex plane. Somewhere you must have a discontinuity where the value changes by 2.pi.i. This "problem" is a motivating example for the beautiful theory of Riemann surfaces.
*There is no number y such that e^y=0, and no sensible way to define log(zero)
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