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.