Impower function

This article describes the formula syntax and usage of the IMPOWER function in Microsoft Excel.

Description

Returns a complex number in x + yi or x + yj text format raised to a power.

Syntax

IMPOWER(inumber, number)

The IMPOWER function syntax has the following arguments:

• Inumber    Required. A complex number you want to raise to a power.

• Number    Required. The power to which you want to raise the complex number.

Remarks

• Use COMPLEX to convert real and imaginary coefficients into a complex number.

• If number is nonnumeric, IMPOWER returns the #VALUE! error value.

• Number can be an integer, fractional, or negative.

• A complex number raised to a power is calculated as follows:

  

  where:

  

  and:

  

  and:

  

Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

Formula	Description	Result
=IMPOWER("2+3i", 3)	2+3i raised to the power of 3 (-46 + 9i)	-46+9.00000000000001i