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denoted by . If is given in polar form as , where and are real numbers with , then is one logarithm of , and all the complex logarithms of are exactly the numbers of the form for integers . These logarithms are equally spaced along a vertical line in the complex plane.
* A complex-valued function , defined on some subset of the set of nonzero complex numbers, satisfying for all in . Such complex logarithm functions are analogous to the real logarithm function

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