IMPOWER function

Applies To
Excel for Microsoft 365 Excel for Microsoft 365 for Mac Excel 2024 Excel 2024 for Mac Excel 2021 Excel 2021 for Mac Excel 2019 Excel 2016

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:
    Formula for raising a complex number to a power in polar form
    where:
    Magnitude of a complex number as the square root of x squared plus y squared
    and:
    Angle theta of a complex number as the arctangent of y divided by x
    and:
    Angle theta is greater than negative pi and at most pi

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