Complex logarithm

（重定向自Imaginary logarithm）

A plot of the multi-valued imaginary part of the complex logarithm function, which shows the branches. As a complex number z goes around the origin, the imaginary part of the logarithm goes up or down. This makes the origin a branch point of the function.

The circles Re(Log z) = constant and the rays Im(Log z) = constant in the complex z-plane.

In complex analysis, a complex logarithm function is an "inverse" of the complex exponential function, just as the real natural logarithm ln x is the inverse of the real exponential function e. Thus, a logarithm of a complex number z is a complex number w such that e = z. The notation for such a w is ln z or log z. Since every nonzero complex number z has infinitely many logarithms, care is required to give such notation an unambiguous meaning.

单词	Imaginary logarithm
释义	Imaginary logarithm 英语百科 Complex logarithm （重定向自Imaginary logarithm） In complex analysis, a complex logarithm function is an "inverse" of the complex exponential function, just as the real natural logarithm ln x is the inverse of the real exponential function e. Thus, a logarithm of a complex number z is a complex number w such that e = z. The notation for such a w is ln z or log z. Since every nonzero complex number z has infinitely many logarithms, care is required to give such notation an unambiguous meaning.
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