Difference between revisions of "Manuals/calci/IMEXP"

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<div style="font-size:30px">'''IMEXP(z)'''</div><br/>
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<div style="font-size:30px">'''IMEXP(ComplexNumber)'''</div><br/>
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*where <math>z</math> is the complex number.
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*<math>ComplexNumber</math> is of the form x+iy.
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**IMEXP(), returns the exponential of a complex number.
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 +
 
 
==Description==
 
==Description==
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*This function gives the exponential of a complex number.  
 
*This function gives the exponential of a complex number.  
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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>.  
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*In <math>IMEXP(ComplexNumber)</math>, <math>ComplexNumber</math> is of the form  <math>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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*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.
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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>.
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*The approximate  value of the constant e=2.718281828459045 and it is equal to <math>e^1</math>.                                                   
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*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'.  
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*Let z be the Complex Number.Then 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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*We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.
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*Here Sin and Cos are trignometric functions. y is angle value in radians.
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*When  imaginary part is '0', it will give the exponent value of the real number. i.e <math>IMEXP(z) = EXP(z)</math> when imaginary number <math>iy</math> is '0'.  
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*The Complex exponential function is denoted by "'''cis(x)'''"(Cosine plus iSine)
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*We can use [[Manuals/calci/COMPLEX | COMPLEX ]] function to convert the real and imaginary coefficients to a complex number.
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==ZOS==
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*The syntax is to calculate IMEXP in ZOS is <math>IMEXP(ComplexNumber)</math>.
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**<math>ComplexNumber</math> is of the form a+bi.
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*For e.g.,IMEXP("0.3-0.54i")
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{{#ev:youtube|nuPmQ8dB3wc|280|center|IMEXP}}
  
 
==Examples==
 
==Examples==
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#IMEXP("2+3i")=-7.315110094901102+1.0427436562359i
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#IMEXP("4-5i")=15.4874305606508+52.355491418482i
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#=IMEXP("2+3i") = -7.315110094901102+1.0427436562359i
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#IMEXP("6")=403.428793492735
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#=IMEXP("4-5i") = 15.4874305606508+52.355491418482i
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#IMEXP("2i")=-0.416146836547142+0.909297426825682i
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#=IMEXP("6") = 403.428793492735+0i
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#IMEXP("0")=1 andIMEXP("0i")=1
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#=IMEXP("2i") = -0.416146836547142+0.909297426825682i
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#=IMEXP("0") = 1+0i and IMEXP("0i") = 1+0i
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==Related Videos==
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{{#ev:youtube|lNEoaXWkzvw|280|center|Exponential Form of Complex Number}}
  
 
==See Also==
 
==See Also==
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==References==
 
==References==
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[http://en.wikipedia.org/wiki/Exponential_function| Exponential function]
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[http://en.wikipedia.org/wiki/Exponential_function   Exponential function]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 15:36, 19 July 2018

IMEXP(ComplexNumber)


  • is of the form x+iy.
    • IMEXP(), returns the exponential of a complex number.


Description

  • This function gives the exponential of a complex number.
  • In , is 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 .
  • Let z be the Complex Number.Then the exponential of a complex number is : .
  • Here Sin and Cos are trignometric functions. y is angle value in radians.
  • When imaginary part is '0', it will give the exponent value of the real number. i.e when imaginary number is '0'.
  • The Complex exponential function is denoted by "cis(x)"(Cosine plus iSine)
  • We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.

ZOS

  • The syntax is to calculate IMEXP in ZOS is .
    • is of the form a+bi.
  • For e.g.,IMEXP("0.3-0.54i")
IMEXP

Examples

  1. =IMEXP("2+3i") = -7.315110094901102+1.0427436562359i
  2. =IMEXP("4-5i") = 15.4874305606508+52.355491418482i
  3. =IMEXP("6") = 403.428793492735+0i
  4. =IMEXP("2i") = -0.416146836547142+0.909297426825682i
  5. =IMEXP("0") = 1+0i and IMEXP("0i") = 1+0i

Related Videos

Exponential Form of Complex Number

See Also

References

Exponential function



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