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30 Απρ 2024 · What is a complex logarithm. Learn how to solve complex logarithmic equations with rules and examples.
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 , defined to be any complex number for which =.
Definition: Complex Log Function. The function \(\text{log} (z)\) is defined as \[\text{log} (z) = \text{log} (|z|) + i \text{arg} (z), \nonumber \] where \(\text{log} (|z|)\) is the usual natural logarithm of a positive real number.
Complex Logarithm. Dive into the fascinating world of engineering maths as you explore the concept of complex logarithm. Grasp the core definition and meaning, broaden your understanding with relevant examples, and discover the fundamental properties of this crucial mathematical element.
14 Αυγ 2021 · Complex functions. Let S be a set of complex numbers. A function f defined on S is a rule that assigns to each z in S a complex number w. The number w is called the value of f at z and is denoted by f(z); that is, w = f(z). The set S is called the domain of definition of f.
In this topic, we have discussed the logarithm of complex numbers, their definition, showed that log e z is a many-valued f n, discussed the General and principal value of log e z, and showed how it works. Moreover, mentioned some important properties of the logarithm and rules of the logarithm.
The logarithm is a multi-valued function, because the angle can be represented in many ways: is the same angle as , but it gives a different imaginary part for . To make single valued, choose a branch: a range for angles. The complex logarithm function, shown geometrically.
