IMPOWER function

The 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.