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.

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