In complex analysis, a complex logarithm function is an "inverse" of the complex exponential function, just as the natural logarithm ln x is the inverse of the real exponential function ex. Thus, a logarithm of z is a complex number w such that ew = z. The notation for such a w is ln z. But because every nonzero complex number z has infinitely many logarithms, care is required to give this notation an unambiguous meaning.
If z = reiθ with r > 0 (polar form), then w = ln (reiθ ), then w = ln r + iθ is one logarithm of z; adding integer multiples of 2πi gives all the others.
Read more about Complex Logarithm: Problems With Inverting The Complex Exponential Function, Definition of Principal Value, Branches of The Complex Logarithm, The Complex Logarithm As A Conformal Map, Applications, Plots of The Complex Logarithm Function (principal Branch)
Famous quotes containing the word complex:
“The money complex is the demonic, and the demonic is God’s ape; the money complex is therefore the heir to and substitute for the religious complex, an attempt to find God in things.”
—Norman O. Brown (b. 1913)