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IMPOWER Function

Excel 2007+

Summary

The Excel IMPOWER function calculates a complex number raised to a specified power, returning the result in standard complex number format (x + yi). This engineering function handles both integer and fractional exponents for complex values.

Syntax

IMPOWER(inumber, number)

Parameters

Parameter	Type	Required	Description
inumber	`Complex Number`	Yes	Complex number in 'x+yi' or 'x+yj' format to raise to power
number	`Number`	Yes	Real number exponent (integer, fractional, or negative)

Using the IMPOWER Function

IMPOWER is crucial for complex number exponentiation in engineering, physics, and advanced mathematics. Use it when working with electrical engineering calculations, signal processing, or any scenario requiring complex powers. Create complex numbers using the COMPLEX function.

Common IMPOWER Examples

Raising Complex Number to Integer Power

=IMPOWER("2+3i",3)

Calculates (2+3i)^3, returning -46+9i for cubic power applications.

Fractional Exponent Example

=IMPOWER("1+i",0.5)

Finds the square root of complex number 1+i.

Negative Exponent

=IMPOWER("3+4i",-1)

Calculates the reciprocal (inverse) of complex number 3+4i.

Frequently Asked Questions

Use the COMPLEX(real_num, i_num) function to convert real/imaginary parts into complex format.

IMPOWER returns #VALUE! error if the number argument cannot be interpreted as a numeric value.

Yes, negative exponents compute the reciprocal of the complex number raised to the positive power.

Common Errors and Solutions

#VALUE!

Cause: Non-numeric exponent provided

Solution: Ensure the number argument is a valid numeric value

#NUM!

Cause: Invalid complex number format

Solution: Use proper 'x+yi' format or COMPLEX function

#NAME?

Cause: IMPOWER not recognized

Solution: Available only in Excel 2007 and later versions

Notes

Use COMPLEX function to build complex numbers from real/imaginary coefficients
Supports both 'i' and 'j' imaginary unit notation
Results maintain Excel's complex number text format
Ideal for electrical engineering (impedance calculations) and physics applications

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2003 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+