Difference between revisions of "Manuals/calci/IMPOWER"

Revision as of 12:48, 21 March 2018

IMPOWER(Complexnumber,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

(z)^{n}=(x+iy)^{n}=r^{n}*e^{in\theta }=r^{n}(cosn\theta +isinn\theta )

where $r={\sqrt {x^{2}+y^{2}}}$ and $\theta =tan^{-1}({\frac {y}{x}})$ , $\theta \in (-\pi ,\pi ]$ .

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(Complexnumber,n), $n$ can be integer, fractional or negative.
If $n$ is non-numeric, function will return error value.

The syntax is to calculate powers of Complex number in ZOS is .
- $Complexnumber$ is of the form $z=x+iy$
- $n$ is the power value.
For e.g.,impower("7-8i",6)

Impower

@@ Line 9: / Line 9: @@
 *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}(\frac{y}{x})</math>, <math>\theta∈(-\pi,\pi]</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.
 *We can use [[Manuals/calci/COMPLEX| COMPLEX]] function to convert real and imaginary number in to a complex number.