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Engineering - IMPOWER Function
Description
The IMPOWER function returns a complex number in x + yi or x + yj text format raised to a power. A complex number raised to a power is calculated as follows −
$$(x+yi)^n=r^ne^{n\theta} = r^n \cos n\theta+ir^n sin n\theta$$
Where −
$$r = \sqrt{x^2+y^2} \: \: and \: \: \theta=\tan^{-1}\left ( \frac{y}{x} \right ) \: \: and \: \: \theta \epsilon(-\pi; \pi]$$
Syntax
IMPOWER (inumber, number)
Arguments
| Argument | Description | Required/ Optional |
|---|---|---|
| Inumber | A complex number you want to raise to a power. | Required |
| Number | The power to which you want to raise the complex number. Number can be an integer, fractional, or negative. |
Required |
Notes
Complex Numbers in Excel are simply stored as text.
When a text string in the format "a + bi" or "a + bj" is supplied to one of Excel's built-in Complex Number Functions, this is interpreted as a complex number.
The complex number functions can accept a simple numeric value, as this is equivalent to a complex number whose imaginary coefficient is equal to 0.
Use COMPLEX to convert real and imaginary coefficients into a complex number.
If inumber is not recognized as a complex number, IMPOWER returns the #NUM! Error.
If number is nonnumeric, IMPOWER returns the #VALUE! Error.
If inumber is a logical value, IMPOWER returns the #VALUE! Error.
Applicability
Excel 2007, Excel 2010, Excel 2013, Excel 2016
Example
