# Manuals/calci/IMPOWER

IMPOWER(Complexnumber,n)

• is of the form
• is the power value.
• IMPOWER(), returns a complex number raised to an integer power.

## 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.
• is the imaginary unit,
• Then the power of a complex number is defined by

where and , .

• 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), can be integer, fractional or negative.
• If is non-numeric, function will return error value.

## ZOS

• The syntax is to calculate powers of Complex number in ZOS is .
• is of the form
• is the power value.
• For e.g.,IMPOWER("7-8i",6)
Impower

## Examples

1. =IMPOWER("4+5i",3) = -235.99999+115i
2. =IMPOWER("9-7i",4) = -14852-8063.999999i
3. =IMPOWER("6",9) = 10077696+0i
4. =IMPOWER("i",10) = -1+0i

IMPOWER