Apr 30, 2024 · The complex logarithm is an extension of the concept of logarithmic functions involving complex numbers (represented by log z). Mathematically, written as log(z) = log(r ⋅ e …

In these notes, we examine the logarithm, exponential and power functions, where the arguments1 of these functions can be complex numbers. In particular, we are interested in …

Complex logarithm Complex power function Definition Properties 1. Complex exponential The exponential of a complex number z = x +iy is defined as exp(z)=exp(x +iy)=exp(x)exp(iy) …

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 …

Jun 11, 2024 · In this article, we will learn about, complex number power formulas, their examples, and others in detail. A number that is written in the form of a+ib where i is an …

Sep 14, 2023 · Complex Logarithm Examples: The complex logarithm of a complex number like \( z = 1 + i \) is calculated as \( Log(z) = ln|z| + i * Arg(z) = ln(\sqrt{2}) + i(\pi/4) \). Complex …

The logarithm function (for complex numbers) is an example of a multiple-valued function. All of the multiple-values of the logarithm have the same real part \(\ln r\) and the imaginary parts all …

May 24, 2024 · Here is the list of all the logarithmic identities. These rules are used to simplify complex logarithmic expressions and solve logarithmic equations involving variables. It states …

Because equation 3.21 yields logarithms of every nonzero complex number, we have defined the complex logarithm function. It is defined for all z 6= 0, and because argz is determined only to …

May 15, 2019 · It is known that if $\alpha$ is a complex number, then for example, the equation $x^2 = \alpha$ has $2$ solutions. In general, there are $n$ values for the $n$-th roots of a …