How to Use IMPOWER function in Google Sheets in 2020?

IMPOWER functionThe IMPOWER function returns a complex number raised to a power.

Parts of a IMPOWER formula

The IMPOWER formula is formatted as =IMPOWER(complex_base, exponent).

Part
Description
Notes

complex_base
The complex number to raise to the exponent power.

May be written as a ∓ bi or a ∓ bj.

exponent
The exponent to raise complex_base to.

Must be a number.

Sample formulas

IMPOWER(“4-3i”,0.5)

IMPOWER(A2,B2)

IMPOWER(“2j”,-7)

Notes

The exponentiation of a complex number is defined as follows:

(a+bi)n = rn(cosθ + isinθ), where
r = √(x2 + y2) and θ = arctan(b/a)

Examples

A
B

1
Formula
Result

2
=IMPOWER(“5+2i”, 3)
65+142i

3
=IMPOWER(“-1-j”, -1)
-0.5+0.5j

4
=IMPOWER(“0.732-5.349i”, -0.138)
0.776914096672106+0.155872432042838i

Related functions

COMPLEX: The COMPLEX function creates a complex number, given real and imaginary coefficients.

IMREAL: Returns the real coefficient of a complex number.

IMAGINARY: Returns the imaginary coefficient of a complex number.

POWER: Returns a number raised to a power.