Documentation/Calc Functions/IMPOWER

Function name:
IMPOWER

Category:
Add-in

Summary:
Calculates the complex number that results from raising a complex number to a real power.

Syntax:
IMPOWER(ComplexNumber; Number)

Returns:
Returns a text string giving the complex number that is obtained by raising the complex number passed as argument to the given power.

Arguments:
ComplexNumber is a string (in quotation marks) representing a complex number in the form a+bi or a+bj, or a reference to a cell containing that string, which is the complex number for which the power is to be calculated. a and b are real numbers.

Number is a real number, or a reference to a cell containing that number, that specifies the power to which ComplexNumber is to be raised.


 * If ComplexNumber does not have an imaginary part (b equal to 0), the real part can be passed to IMPOWER as a number rather than a string.
 * If both real and imaginary parts of ComplexNumber are 0, and Number <= 0, then IMPOWER reports an invalid argument error (Err:502).
 * If ComplexNumber is not a valid complex number, IMPOWER reports an invalid argument error (Err:502).
 * If Number is non-numeric, then IMPOWER reports a #VALUE! error.

Details specific to IMPOWER function
A complex number z expressed in its rectangular form z=a+bi can be re-written in polar form as z=r(cosφ+isinφ), where r is the absolute value of the complex number and φ is its argument.

After converting ComplexNumber to polar form, IMPOWER solves the following equation: where p is the required power given by the supplied value of the Number parameter.

Calc does not support the alternative syntax of  that is suggested in ODF 1.2.

Related LibreOffice functions:
IMEXP

IMLN

IMLOG10

IMLOG2

IMSQRT

ODF standard:
Section 6.8.17, part 2

Equivalent Excel functions:
IMPOWER