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.                                                                     *So the exponential of a complex number is : IMEXP(z)=e^z=e^(x+iy)=e^x.e^iy=e^x.(cosy+isiny).  
+
*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

  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