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.