## Excel IMPOWER function

The IMPOWER function returns a complex number raised to a given power.

#### Syntax

IMPOWER(inumber, number)

#### Arguments

• Inumber (required): The complex number you want to raise to a given power.
• Number (required): The power to which you want to raise the complex number. It can be supplied as any of the following:
-- An integer;
-- A fractional;
-- A negative number.

#### Remarks

1. The #VALUE! error occurs if any of the following conditions is met:
-- “inumber” is a logical value;
-- “number” is non-numeric.
2. The #NUM! error occurs if “inumber” cannot be recognized as a complex number.
3. The equation for the IMPOWER function is as follows:

where

and:

and:

#### Return value

It returns a complex number as text.

#### Example

As shown in the table below, to raise the complex numbers listed in column B to a certain power listed in column C, you can apply the IMPOWER function as follows.

Select a cell (says D6 in this case), enter the formula below and press the Enter key to get the first result. Select this result cell and then drag its AutoFill Handle down to get other results.

=IMPOWER(B6,C6)

Notes:

1) The complex number and the power can be directly entered into the formula. The formula in D6 can be changed to:

=IMPOWER("4+2i",2)

Tips: The complex number needs to be enclosed in double quotation marks.
2) The IMPOWER function accepts only lowercase “i” and “j”.

#### Related Functions

Excel COMPLEX function
The COMPLEX function converts real and imaginary coefficients to a complex number of the form x + yi or x + yj.

Excel IMABS function
The IMABS function gets the absolute value of a complex number in the form x + yi or x + yj.

Excel imaginary function
The IMAGINARY function gets the imaginary coefficient of a complex number in the form x + yi or x + yj.

Excel improduct Function
The IMPRODUCT function returns the product of 1 to 255 complex numbers in x + yi or x + yj text format.

Excel BITAND function
The IMREAL function returns the real coefficient of a complex number in the form x + yi or x + yj.

Excel IMSUB function
The IMSUB function returns the difference of two complex numbers in x + yi or x + yj text format.

Excel IMSUM function
The IMSUM function returns the sum of two or more complex numbers in x + yi or x + yj text format.

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