plz explain me all about Logarithms of complex Quantities .
1
Expert's answer
2012-10-17T09:36:08-0400
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 e^x. Thus, a logarithm of z is a complex number w such that e^w = 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 = r*e^(i*θ) with r > 0 (polar form), then w = ln(r) + i*θ is one logarithm of z; adding integer multiples of 2πi gives all the others.
The expert did excellent work as usual and was extremely helpful for me.
"Assignmentexpert.com" has experienced experts and professional in the market. Thanks.
Comments