Difference between revisions of "Manuals/calci/IMLN"

Revision as of 05:14, 16 December 2013

IMLN(z)

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 :

$ln(z)=w=ln(|z|)+iarg(z)=ln({\sqrt {x^{2}+y^{2}}}+itan^{-1}({\frac {y}{x}})$ 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.

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

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 *In IMLN(z), where <math>z</math> is the complex number in the form of <math>x+iy</math>. i.e <math>x</math> & <math>y</math> are the real numbers.
 *<math>I</math> imaginary unit <math>i=\sqrt{-1}</math>.
-*A logarithm of <math>z</math> is a complex number w such that <math>z = e^w</math> and it is denoted by <math>ln(z)</math>.
+*A logarithm of <math>z</math> is a complex number <math>w</math> such that <math>z = e^w</math> and it is denoted by <math>ln(z)</math>.
 *If <math>z = x+iy</math> with <math>x</math> & <math>y</math> are real numbers then natural logarithm of a complex number :
 <math>ln(z)= w = ln(|z|) + iarg(z) = ln(\sqrt{x^2+y^2}+itan^{-1}(\frac{y}{x})</math>                                                                                                                            adding integer multiples of <math>2\pi i</math> gives all the others.