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Engineering function
IMPOWER
Returns a complex number raised to an integer power.
Rarely usedDifficulty 1500 · AdvancedUsage rank #498 of 520
When to use it
A complex number raised to a real power.
The shape of it
- Syntax
=IMPOWER(inumber, number)
Worked examples
Cube
=IMPOWER("2+3i",3) → -46+9i
Cubed.
i squared
=IMPOWER("i",2) → -1
i squared.
Square
=IMPOWER("1+i",2) → 2i
Squaring a 45° number doubles the angle.
Worth knowing
- Fractional powers give principal roots: IMPOWER("-4",0.5) is 2i, the same as IMSQRT.
- Works in polar form under the hood.
- Result is text.
Where it goes wrong
- #VALUE! for invalid text or a non-numeric power.
- Small floating-point residues appear in results that should be exact.
Related
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