Author: Oscar Cronquist Article last updated on November 14, 2022

How to use the IMPOWER function

The IMPOWER function calculates a complex number raised to a given power in x + yi or x + yj text format.

The letter j is used in electrical engineering to distinguish between the imaginary value and the electric current.

A complex number raised to a given power is calculated like this:

C = x + yi

IMPOWER(C) = (x+y)n = rneinθ = rncos nθ+irnsin nθ

The IMABS function calculates r, the IMARGUMENT function calculates θ.

1. IMPOWER Function Syntax

IMPOWER(inumber, number)

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2. IMPOWER Function Arguments

inumber Required. A complex number in x+yi or x+yj text format.
number Required. The power you want to raise the complex number to. Integer, fractional, or negative values are allowed.

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3. IMPOWER function example

How to use the IMPOWER function

The image above demonstrates a formula in cell D3 that calculates a complex number specified in cell C3 raised to the power of 2.

Formula in cell C3:

=IMPOWER(B3, 2)

3.1 Explaining formula

Step 1 - Populate arguments

IMPOWER(inumber, number)

becomes

IMPOWER(B3, 2)

Step 2 - Evaluate the IMPOWER function

IMPOWER(B3, 2)

becomes

IMPOWER("1+2i", 2)

and returns

-3+4i

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