Manuals/calci/IMLN

IMLN(z)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z} is the complex number is of the form Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x+iy}

Description

This function gives the natural logarithm of a complex number.
In IMLN(z),Where z is the complex number in the form of "x+iy".i.e. x&y are the real numbers.
'I' imaginary unit .i=sqrt(-1).
A logarithm of z is a complex number w such that z = e^w and it is denoted by ln(z).
If z = x+iy with x&y are real numbers then natural logarithm of a complex number : Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ln(z)= w = ln(|z|) + iarg(z) =ln(sqrt(x^2+y^2)+itan^-1(y/x} adding integer multiples of 2πi gives all the others.
We can use COMPLEX function to convert real and imaginary number in to a complex number.

IMLN("3-2i")=1.28247467873077-0.588002603547568i
IMLN("6+7i")=2.22132562824516+0.862170054667226i
IMLN("4")=1.38629436111989 But calci is not considering the zero value of imaginary value of z.
IMLN("10i")=2.30258509299405+1.5707963267949i