Difference between revisions of "Manuals/calci/IMPOWER"
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*<math>Complexnumber</math> is of the form <math>z=x+iy</math> | *<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. | ||
| + | **IMPOWER(), returns a complex number raised to an integer power. | ||
==Description== | ==Description== | ||
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*Then the power of a complex number is defined by | *Then the power of a complex number is defined by | ||
:<math>(z)^n=(x+iy)^n=r^n*e^{in\theta}=r^n(cosn\theta+isinn\theta)</math> | :<math>(z)^n=(x+iy)^n=r^n*e^{in\theta}=r^n(cosn\theta+isinn\theta)</math> | ||
| − | where <math>r=\sqrt{x^2+y^2}</math> and <math>\theta=tan^{-1}(\frac{y}{x})</math>, <math>\ | + | 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. | ||
*We can use [[Manuals/calci/COMPLEX| COMPLEX]] function to convert real and imaginary number in to a complex number. | *We can use [[Manuals/calci/COMPLEX| COMPLEX]] function to convert real and imaginary number in to a complex number. | ||
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**<math>Complexnumber</math> is of the form <math>z=x+iy</math> | **<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. | ||
| − | *For e.g., | + | *For e.g.,IMPOWER("7-8i",6) |
{{#ev:youtube|QRkmmsadQhA|280|center|Impower}} | {{#ev:youtube|QRkmmsadQhA|280|center|Impower}} | ||
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#=IMPOWER("4+5i",3) = -235.99999+115i | #=IMPOWER("4+5i",3) = -235.99999+115i | ||
#=IMPOWER("9-7i",4) = -14852-8063.999999i | #=IMPOWER("9-7i",4) = -14852-8063.999999i | ||
| − | #=IMPOWER("6",9) = 10077696 | + | #=IMPOWER("6",9) = 10077696+0i |
| − | #=IMPOWER("i",10) = -1+ | + | #=IMPOWER("i",10) = -1+0i |
==Related Videos== | ==Related Videos== | ||
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==References== | ==References== | ||
[http://en.wikipedia.org/wiki/De_Moivre's_formula De Moivre's formula] | [http://en.wikipedia.org/wiki/De_Moivre's_formula De Moivre's formula] | ||
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| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
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.
is of the form 
is the power value.
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
is the imaginary unit, 
where and , .
and 
, ![{\displaystyle \theta \in (-\pi ,\pi ]}](https://wikimedia.org/api/rest_v1/media/math/render/png/2742d923047f035ec3e8db8259485fda0629104b)
.
- 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)
.
Examples
- =IMPOWER("4+5i",3) = -235.99999+115i
- =IMPOWER("9-7i",4) = -14852-8063.999999i
- =IMPOWER("6",9) = 10077696+0i
- =IMPOWER("i",10) = -1+0i
Related Videos
See Also
References