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# Answer to Question #16394 in Trigonometry for soni sharma

Question #16394
plz explain me all about Logarithms of complex Quantities .
Expert's answer
In complex analysis, a complex logarithm function is an &quot;inverse&quot; 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*&theta;) with r &gt; 0 (polar form), then w = ln(r) + i*&theta; is one logarithm of z; adding integer multiples of 2&pi;i gives all the others.

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