Difference between revisions of "Manuals/calci/IMEXP"

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

Revision as of 06:00, 25 November 2013

IMEXP(z)


  • where is the complex number.

Description

  • This function gives the exponential of a complex number.
  • In , is the complex number of the form , & are real numbers & is the imaginary unit. .
  • Euler's formula states that , for any real number and is the base of the natural logarithm.
  • The approximate value of the constant e=2.718281828459045 and it is equal to . So the exponential of a complex number is : .
  • When imaginary part is '0', 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 imaginary 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