Manuals/calci/IMPOWER
IMPOWER(z,n)
- is the complex number is of the form
- 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.
- is the imaginary unit,
- Then the power of a complex number is defined by
where and , 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(z,n), can be integer, fractional or negative.
- If is non-numeric, function will return error value.
Examples
- =IMPOWER("4+5i",3) = -235.99999+115i
- =IMPOWER("9-7i",4) = -14852-8063.999999i
- =IMPOWER("6",9) = 10077696
- =IMPOWER("i",10) = -1+6.1257422745431E-16i