Difference between revisions of "Manuals/calci/IMEXP"

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<div style="font-size:30px">'''IMEXP(z)'''</div><br/>
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*where 'z' is the complex number.
 +
==Description==
 +
*This function gives the exponential of a complex number.
 +
*Here IMEXP(z),where z is the complex number of the form  z=x+iy,
 +
*x&y are real numbers&I is the imaginary unit,i=sqrt(-1).
 +
*Euler's formula states that e^ix=cosx+isinx, for any real number x and e is the base of the natural logarithm.
 +
*The approximate  value of the constant e=2.718281828459045 and it is equal to e^1.                                                                    *So the exponential of a complex number is : IMEXP(z)=e^z=e^(x+iy)=e^x.e^iy=e^x.(cosy+isiny). *=e^x.cosy+ie^x.siny. When  imaginary part is '0' then it will give the exponent value of the real number. *i.e.IMEXP(z)=EXP(z) when imaginary number (iy) is '0'.
 +
*We can use COMPLEX function to convert the real and imginary coefficients to a complex number.
  
Syntax
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==Examples==
 +
#IMEXP("2+3i")=-7.315110094901102+1.0427436562359i
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#IMEXP("4-5i")=15.4874305606508+52.355491418482i
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#IMEXP("6")=403.428793492735
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#IMEXP("2i")=-0.416146836547142+0.909297426825682i
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#IMEXP("0")=1 andIMEXP("0i")=1
  
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==See Also==
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*[[Manuals/calci/COMPLEX  | COMPLEX ]]
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*[[Manuals/calci/IMAGINARY  | IMAGINARY ]]
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*[[Manuals/calci/IMREAL  | IMREAL ]]
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*[[Manuals/calci/EXP  | EXP ]]
  
Remarks
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==References==
 
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[http://en.wikipedia.org/wiki/Exponential_function| Exponential function]
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Examples
 
 
 
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<div id="8SpaceContent" align="left"><div class="ZEditBox" align="justify">'''<font face="Times New Roman">''''''''''''<font size="6"> </font>''' '''''''''</font>'''</div></div>
 
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<font size="5">Description</font>
 
 
 
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<font color="#484848"><font face="Arial, sans-serif"><font size="2">This function calculates the exponential of a complex number in a+ bj or a+ bj text format.</font></font></font>
 
 
 
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<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify"><font size="6">'''<font face="Arial">IMEXP</font>'''</font></div></div>
 
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<font color="#484848"><font face="Arial, sans-serif"><font size="2">The exponential of a complex number is: </font></font></font>
 
 
 
<font color="#484848">IMEXP(z)=e<sup>(x+yi)</sup> = e<sup>x</sup> e<sup>yi</sup> =e<sup>x</sup> (cos y + i sin y)</font>
 
 
 
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<font color="#484848"><font face="Arial, sans-serif"><font size="2">'''IMEXP'''</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">(</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">'''IN'''</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">)</font></font></font>
 
 
 
<font color="#484848"><font face="Arial, sans-serif"><font size="2">where IN</font></font></font><font color="#484848"><font face="Arial, sans-serif"><font size="2">  is the complex number.</font></font></font>
 
 
 
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| Column1
 
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| class="sshl_f" | 3.9923240484412714+6.217676312367968i
 
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<div id="12Space_Handle" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="12Space_Copy" title="Click and Drag over to AutoFill other cells."></div>
 
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<div align="left">[[Image:calci1.gif]]</div></div>
 
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<font color="#484848"><font face="Arial, sans-serif"><font size="2">Let's see an example</font></font></font>
 
 
 
<font color="#484848"><font face="Arial, sans-serif"><font size="2"><nowiki>=IMEXP(“2+i”) is3.992+6.2177i</nowiki></font></font></font>
 
 
 
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Revision as of 06:48, 23 November 2013

IMEXP(z)


  • where 'z' is the complex number.

Description

  • This function gives the exponential of a complex number.
  • Here IMEXP(z),where z is the complex number of the form z=x+iy,
  • x&y are real numbers&I is the imaginary unit,i=sqrt(-1).
  • Euler's formula states that e^ix=cosx+isinx, for any real number x and e is the base of the natural logarithm.
  • The approximate value of the constant e=2.718281828459045 and it is equal to e^1. *So the exponential of a complex number is : IMEXP(z)=e^z=e^(x+iy)=e^x.e^iy=e^x.(cosy+isiny). *=e^x.cosy+ie^x.siny. When imaginary part is '0' then it will give the exponent value of the real number. *i.e.IMEXP(z)=EXP(z) when imaginary number (iy) is '0'.
  • We can use COMPLEX function to convert the real and imginary coefficients to a complex number.

Examples

  1. IMEXP("2+3i")=-7.315110094901102+1.0427436562359i
  2. IMEXP("4-5i")=15.4874305606508+52.355491418482i
  3. IMEXP("6")=403.428793492735
  4. IMEXP("2i")=-0.416146836547142+0.909297426825682i
  5. IMEXP("0")=1 andIMEXP("0i")=1

See Also

References

Exponential function