Difference between revisions of "Manuals/calci/IMEXP"
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| − | <div | + | <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. | ||
| − | + | ==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 | ||
| − | + | ==See Also== | |
| − | + | *[[Manuals/calci/COMPLEX | COMPLEX ]] | |
| − | + | *[[Manuals/calci/IMAGINARY | IMAGINARY ]] | |
| + | *[[Manuals/calci/IMREAL | IMREAL ]] | ||
| + | *[[Manuals/calci/EXP | EXP ]] | ||
| − | + | ==References== | |
| − | + | [http://en.wikipedia.org/wiki/Exponential_function| Exponential function] | |
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Revision as of 05:48, 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
- 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