Manuals/calci/IMLOG

IMLOG (ComplexNumber,Base)

Description

This function shows the log value of a complex number.
In $IMLOG(ComplexNumber,Base)$ , $ComplexNumber$ is any complex number.
$Base$ is the base value of a Log values.
A complex logarithm function is an "inverse" of the complex exponential function.
It is same as the real natural logarithm ln x is the inverse of the real exponential function.
Thus, a logarithm of a complex number z is a complex number w such that $e^{w}=z$ .
The notation for such a $w$ is $lnz$ or $logz$ .
If $z=re^{i\theta }$ with $r>0$ which is in Polar form, then $w=lnr+i\theta$ is one logarithm of z.
Adding integer multiples of 2πi gives all the others.
The complex exponential function is not injective, because $e^{w+2\pi i}=e^{w}$ for any w, since adding iθ to w has the effect of rotating $e^{w}$ counterclockwise θ radians.
So the points $.....w-4\pi i,w-2\pi i,w,w+2\pi i,w+4\pi i....$