Calculator for calculating the natural logarithm (log) of a complex number
The function returns the natural logarithm (base e) of a specified complex number.
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In the following description,\(z\) stands for the complex number.
\(x\) stands for the real value \(Re\) and \(y\) for the imaginary value \(Im\).
\(\displaystyle ln(z) = \frac{1}{2} · ln\left(x^2 + y^2\right) + atan\left(\frac{y}{x}\right)\)
Example
\(ln(z) = ln(3+5i)\)
\(\displaystyle Re = \frac{1}{2} · ln\left(3^2 + 5^2\right) = \frac{1}{2} · ln(9 + 25) =1.763\)
\(\displaystyle Im = atan\left(\frac{5}{3}\right) = 1.030\)
\(\displaystyle ln(3+5i) = 1.763+1.030i\)
The result for \(\displaystyle Im \) is given in radians.
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