Difference between revisions of "Manuals/calci/IMPOWER"

Revision as of 21:47, 18 December 2013

IMPOWER(z,n)

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.
i'is the imaginary unit, $i={\sqrt {-1}}$
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^{inθ}=r^n(cosnθ+isinnθ)} where $r={\sqrt {x^{2}+y^{2}}}$ . and Failed to parse (syntax error): {\displaystyle θ=tan^-1(y/x)} , θ∈(-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), n can be integer, fractional or negative.
suppose n is nonnumeric , this function will returns the error value.

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 *DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.
 *i'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^{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()].
+*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∈(-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.