Difference between revisions of "Manuals/calci/IMPOWER"

Revision as of 07:09, 13 March 2017

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 $\theta =tan^{-1}({\frac {y}{x}})$ , Failed to parse (syntax error): {\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(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

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 ==References==
 [http://en.wikipedia.org/wiki/De_Moivre's_formula  De Moivre's formula]
+*[[Z_API_Functions | List of Main Z Functions]]
+*[[ Z3 |   Z3 home ]]