Complex logarithm

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In mathematics, a complex logarithm is a generalization of the natural logarithm to nonzero complex numbers. The term refers to one of the following, which are strongly related: A complex logarithm of a nonzero complex number z {\displaystyle z} , defined to be any complex number w {\displaystyle w} for which e w = z {\displaystyle e^{w}=z} . Such a number w {\displaystyle w} is denoted by log ⁡ z {\displaystyle \log z} . If z {\displaystyle z} is given in polar form as z = r e i θ {\displaystyle z=re^{i\theta }}...

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