Difference between revisions of "Manuals/calci/IMLN"

Latest revision as of 15:30, 16 July 2018

IMLN(Complexnumber)

This function gives the Natural Logarithm of a complex number.
In $IMLN(Complexnumber)$ , where Complexnumber is in the form of $z=x+iy$ . i.e $x$ & $y$ are the real numbers.
And $I$ is the imaginary unit $i={\sqrt {-1}}$ .
Normally Complex logarithm function is an inverse of the Complex exponential function.
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 :

$ln(z)=w=ln(|z|)+iarg(z)=ln({\sqrt {x^{2}+y^{2}}}+itan^{-1}({\frac {y}{x}})$ adding integer multiples of $2\pi i$ gives all the others.

We can use COMPLEX function to convert real and imaginary number in to a complex number.

The syntax is to calculate the natural logarithm of a complex number in ZOS is .
- $Complexnumber$ is of the form $z=x+iy$
For e.g.,IMLN("10+17i")

Natural Logarithm of a Complex Number

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 <div style="font-size:30px">'''IMLN(Complexnumber)'''</div><br/>
-*<math>Complexnumber</math> is of the form <math>z=x+iy</math>
+*<math>Complexnumber</math> is of the form <math>z=x+iy</math>.
+**IMLN(),returns the natural logarithm of a complex number.
 ==Description==