Difference between revisions of "Manuals/calci/IMLN"
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| − | <div style="font-size:30px">'''IMLN( | + | <div style="font-size:30px">'''IMLN(Complexnumber)'''</div><br/> |
| − | *<math> | + | *<math>Complexnumber</math> is of the form <math>z=x+iy</math> |
==Description== | ==Description== | ||
*This function gives the Natural Logarithm of a complex number. | *This function gives the Natural Logarithm of a complex number. | ||
| − | *In IMLN( | + | *In <math>IMLN(Complexnumber)</math>, where Complexnumber is in the form of <math>z=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>. | + | *And <math>I</math> is the imaginary unit <math>i=\sqrt{-1}</math>. |
| + | *Normally Complex logarithm function is an inverse of the Complex exponential function. | ||
*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>. | *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 : | *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. | <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. | *We can use COMPLEX function to convert real and imaginary number in to a complex number. | ||
| + | |||
| + | ==ZOS Section== | ||
| + | *The syntax is to calculate the natural logarithm of a complex number in ZOS is <math>IMLN(Complexnumber)</math>. | ||
| + | **<math>Complexnumber</math> is of the form <math>z=x+iy</math> | ||
| + | *For e.g., | ||
==Examples== | ==Examples== | ||
Revision as of 00:06, 23 June 2014
IMLN(Complexnumber)
- is of the form
is of the form 
Description
- This function gives the Natural Logarithm of a complex number.
- In , where Complexnumber is in the form of . i.e & are the real numbers.
- And is the imaginary unit .
- Normally Complex logarithm function is an inverse of the Complex exponential function.
- A logarithm of is a complex number such that and it is denoted by .
- If with & are real numbers then natural logarithm of a complex number :
, where Complexnumber is in the form of 
& 
are the real numbers.
is the imaginary unit 
.
is a complex number 
such that 
and it is denoted by 
.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.
ZOS Section
- The syntax is to calculate the natural logarithm of a complex number in ZOS is .
- is of the form
- For e.g.,
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