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 = r n (cosθ + isinθ), where
- r = √(x 2 + y 2 ) 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.
