Difference between revisions of "Manuals/calci/IMLN"
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==Description== | ==Description== | ||
| − | *This function gives the | + | *This function gives the Natural Logarithm of a complex number. |
| − | *In IMLN(z), | + | *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 z is a complex number w such that z = e^w and it is denoted by ln(z). | + | *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>. |
| − | *If z = x+iy with x&y are real numbers then natural logarithm of a complex number : <math>ln(z)= w = ln(|z|) | + | *If <math>z = x+iy</math> with <math>x<math> & <math>y</math> are real numbers then natural logarithm of a complex number : |
| − | *We can use COMPLEX function to convert | + | <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. |
| + | *We can use COMPLEX function to convert real and imaginary number in to a complex number. | ||
| + | |||
==Examples== | ==Examples== | ||
Revision as of 05:12, 16 December 2013
IMLN(z)
- is the complex number is of the form
is the complex number is of the form 
Description
- This function gives the Natural Logarithm of a complex number.
- In IMLN(z), where . i.e Failed to parse (syntax error): {\displaystyle x<math> & <math>y<math> are the real numbers. *<math>I} imaginary unit is a complex number w such that and it is denoted by .
- If with Failed to parse (syntax error): {\displaystyle x<math> & <math>y} are real numbers then natural logarithm of a complex number :
. i.e Failed to parse (syntax error): {\displaystyle x<math> & <math>y<math> are the real numbers. *<math>I}
imaginary unit 
is a complex number w such that 
and it is denoted by 
.
with Failed to parse (syntax error): {\displaystyle x<math> & <math>y}
are real numbers then natural logarithm of a complex number :adding integer multiples of gives all the others.
adding integer multiples of 
gives all the others.
- We can use COMPLEX function to convert real and imaginary number in to a complex number.
Examples
- 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
See Also