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| − | <div id=" 16SpaceContent" align="left"><div class= "ZEditBox" align= "justify"> | + | <div style="font-size:30px">'''IMEXP(z)'''</div><br/> |
| | + | *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. |
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| − | Syntax
| + | ==Examples== |
| | + | #IMEXP("2+3i")=-7.315110094901102+1.0427436562359i |
| | + | #IMEXP("4-5i")=15.4874305606508+52.355491418482i |
| | + | #IMEXP("6")=403.428793492735 |
| | + | #IMEXP("2i")=-0.416146836547142+0.909297426825682i |
| | + | #IMEXP("0")=1 andIMEXP("0i")=1 |
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| − | </div></div>
| + | ==See Also== |
| − | ----
| + | *[[Manuals/calci/COMPLEX | COMPLEX ]] |
| − | <div id="4SpaceContent" align="left"><div class="ZEditBox" align="justify">
| + | *[[Manuals/calci/IMAGINARY | IMAGINARY ]] |
| | + | *[[Manuals/calci/IMREAL | IMREAL ]] |
| | + | *[[Manuals/calci/EXP | EXP ]] |
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| − | Remarks
| + | ==References== |
| − | | + | [http://en.wikipedia.org/wiki/Exponential_function| Exponential function] |
| − | </div></div>
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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>
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| − | <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>
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| − | <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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| − | <font color="#484848"><font face="Arial, sans-serif"><font size="2">Let's see an example</font></font></font>
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| − | <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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