Difference between revisions of "Manuals/calci/IMPOWER"
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*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. | ||
| − | *i | + | *<math>i</math> is the imaginary unit, <math>i=\sqrt{-1}</math> |
| − | *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> where <math>r=\sqrt{x^2+y^2}</math> | + | *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> | ||
| + | where <math>r=\sqrt{x^2+y^2}</math> and <math>\theta=tan^-1(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 22:36, 23 December 2013
IMPOWER(z,n)
- 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 z} is the complex number is of the form 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 x+iy}
- 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 n} 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.
- 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 i} is the imaginary unit, 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 i=\sqrt{-1}}
- Then the power of a complex number is defined by
- 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 (z)^n=(x+iy)^n=r^n*e^{in\theta}=r^n(cosn\theta+isinn\theta)}
where 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 r=\sqrt{x^2+y^2}} 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=tan^-1(y/x)} , 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), 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 n} can be integer, fractional or negative.
- If 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 n} 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