Manuals/calci/IMPOWER

IMPOWER(Complexnumber,n)

$Complexnumber$ is of the form $z=x+iy$
$n$ 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.
$i$ 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 (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(Complexnumber,n), $n$ can be integer, fractional or negative.
If $n$ is non-numeric, function will return error value.

ZOS

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)