Difference between revisions of "Manuals/calci/IMPOWER"
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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(y | + | where <math>r=\sqrt{x^2+y^2}</math> and <math>\theta=tan^{-1}(\frac{y}{x})</math>, <math>\theta∈(-\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. | ||
Revision as of 23:16, 25 December 2013
IMPOWER(z,n)
- is the complex number is of the form
- is the power value.
is the complex number 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 , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta∈(-\pi,\pi]} .
and 
, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta∈(-\pi,\pi]}
.
- 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(z,n), can be integer, fractional or negative.
- If is non-numeric, function will return error value.
Examples
- =IMPOWER("4+5i",3) = -235.99999+115i
- =IMPOWER("9-7i",4) = -14852-8063.999999i
- =IMPOWER("6",9) = 10077696
- =IMPOWER("i",10) = -1+6.1257422745431E-16i