Difference between revisions of "Manuals/calci/IMPOWER"

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<div style="font-size:30px">'''IMPOWER(z,n)'''</div><br/>
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<div style="font-size:30px">'''IMPOWER(Complexnumber,n)'''</div><br/>
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*<math>z</math> is the complex number is of the form <math>x+iy</math>  
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*<math>Complexnumber</math> is of the form <math>z=x+iy</math>  
 
*<math>n</math> is the power value.
 
*<math>n</math> is the power value.
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**IMPOWER(), returns a complex number raised to an integer power.
  
 
==Description==
 
==Description==
 
*This function gives the value of powers of complex number.
 
*This function gives the value of powers of complex number.
 
*DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.
 
*DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.
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*i'is the imaginary unit, <math>i=\sqrt{-1}</math>
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*<math>i</math> is the imaginary unit, <math>i=\sqrt{-1}</math>
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*Then the power of a complex number is defined by <math>(z)^n=(x+iy)^n=r^n*e^{inθ}=r^n(cosnθ+isinnθ)</math> where <math>r=\sqrt{x^2+y^2}</math>. and  <math>θ=tan^-1(y/x)</math>, θ∈(is belongs to) (-Pi(),Pi()].  
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*Then the power of a complex number is defined by
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:<math>(z)^n=(x+iy)^n=r^n*e^{in\theta}=r^n(cosn\theta+isinn\theta)</math>  
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where <math>r=\sqrt{x^2+y^2}</math> and  <math>\theta=tan^{-1}(\frac{y}{x})</math>, <math>\theta \isin (-\pi,\pi]</math>.  
 
*This formula is called DeMoivre's theorem of complex numbers.  
 
*This formula is called DeMoivre's theorem of complex numbers.  
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*We can use COMPLEX function to convert   real and imaginary number in to a complex number.  
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*We can use [[Manuals/calci/COMPLEX| COMPLEX]] function to convert real and imaginary number in to a complex number.  
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*In IMPOWER(z,n), n can be integer, fractional or negative.  
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*In IMPOWER(Complexnumber,n), <math>n</math> can be integer, fractional or negative.  
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*suppose n is nonnumeric , this function will returns the error value.
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*If <math>n</math> is non-numeric, function will return error value.
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==ZOS==
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*The syntax is to calculate powers of Complex number in ZOS is <math>IMPOWER(Complexnumber,n)</math>.
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**<math>Complexnumber</math>  is of the form <math>z=x+iy</math>
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**<math>n</math> is the power value.
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*For e.g.,IMPOWER("7-8i",6)
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{{#ev:youtube|QRkmmsadQhA|280|center|Impower}}
  
 
==Examples==
 
==Examples==
  
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#IMPOWER("4+5i",3)=-235.99999+115i
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#=IMPOWER("4+5i",3) = -235.99999+115i
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#IMPOWER("9-7i",4)=-14852-8063.999999i
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#=IMPOWER("9-7i",4) = -14852-8063.999999i
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#IMPOWER("6",9)=10077696(EXCEL)=10077696-8i(CALCI)
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#=IMPOWER("6",9) = 10077696+0i
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#IMPOWER("i",10)=-1-16i(CALCI)=-1+6.1257422745431E-16i
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#=IMPOWER("i",10) = -1+0i
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==Related Videos==
  
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*For imaginary value '0' is not accepting in CALCI.
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{{#ev:youtube|dl_9NC_J6yo|280|center|IMPOWER}}
  
 
==See Also==
 
==See Also==
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*[[Manuals/calci/IMREAL  | IMREAL ]]
 
*[[Manuals/calci/IMREAL  | IMREAL ]]
 
*[[Manuals/calci/IMSUM  | IMSUM ]]
 
*[[Manuals/calci/IMSUM  | IMSUM ]]
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*[[Manuals/calci/COMPLEX  | COMPLEX ]]
 
*[[Manuals/calci/COMPLEX  | COMPLEX ]]
  
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==References==
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[http://en.wikipedia.org/wiki/De_Moivre's_formula  De Moivre's formula]
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 +
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*[[Z_API_Functions | List of Main Z Functions]]
  
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==References==
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*[[ Z3 |  Z3 home ]]
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[http://en.wikipedia.org/wiki/Binary_logarithm  Binary Logarithm]
 

Latest revision as of 04:02, 2 November 2020

IMPOWER(Complexnumber,n)


  • is of the form
  • is the power value.
    • IMPOWER(), returns a complex number raised to an integer power.

Description

  • This function gives the value of powers of complex number.
  • DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.
  • is the imaginary unit,
  • Then the power of a complex number is defined by

where and , .

  • This formula is called DeMoivre's theorem of complex numbers.
  • We can use COMPLEX function to convert real and imaginary number in to a complex number.
  • In IMPOWER(Complexnumber,n), can be integer, fractional or negative.
  • If is non-numeric, function will return error value.

ZOS

  • The syntax is to calculate powers of Complex number in ZOS is .
    • is of the form
    • is the power value.
  • For e.g.,IMPOWER("7-8i",6)
Impower

Examples

  1. =IMPOWER("4+5i",3) = -235.99999+115i
  2. =IMPOWER("9-7i",4) = -14852-8063.999999i
  3. =IMPOWER("6",9) = 10077696+0i
  4. =IMPOWER("i",10) = -1+0i

Related Videos

IMPOWER

See Also

References

De Moivre's formula


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