Manuals/calci/IMPOWER

IMPOWER(z,n)

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 $\theta =tan^{-}1(y/x)$ , 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), $n$ can be integer, fractional or negative.
If $n$ is non-numeric, function will return error value.