Difference between revisions of "Manuals/calci/IMEXP"
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*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). | *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. | *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. | + | *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'. | *=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. | *We can use COMPLEX function to convert the real and imginary coefficients to a complex number. | ||
Revision as of 06:56, 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