IMPOWER Function (LibreOffice Calc)

IMPOWER raises a complex number to a real-number power. It is the complex-number analogue of the real-valued POWER operation, producing an answer encoded as a complex text string. For example, (2+3i)² = -5+12i, so:

=IMPOWER("2+3i";2)

Expected mathematically and observed in native Calc 25.2.3.2: -5+12i. The legacy guide’s summary, “Returns a complex number raised to a real power,” remains correct.

=IMPOWER(ComplexNumber; Number)

ComplexNumber — Required. Complex string such as "2+3i", "2+3j", a referenced cell containing complex text, or COMPLEX(real;imaginary). The real-only numeric form also works.

Number — Required. The real numeric exponent. Integer, zero, negative and fractional exponents are possible; no default is provided.

Order matters: the complex base comes first; the real exponent comes second. The English Calc formula separator is usually the semicolon, as in the syntax above. Microsoft Excel’s English documentation uses a comma, and other locales/settings may differ. Both i and j suffixes are valid and should not be mixed accidentally in a dataset. The official current page displayed LibreOffice 26.8 Help when checked 2026-10-11; native examples were run in Calc 25.2.3.2. There is no substantiated claim here about the first release of this function or web/mobile editions.

Enter the following into an empty sheet:

On a narrow screen, scroll this table sideways to see every column.

In E2 enter:

=IMPOWER(A2;D2)

Expected / observed: -5+12i. Expand the product as (2+3i)(2+3i) = (4-9)+12i to verify manually. The result is a text-formatted complex number; =ISTEXT(IMPOWER(1;2)) was TRUE in the native run.

The cube of the same input is useful for understanding precision:

=IMPOWER("2+3i";3)

Expected exactly: -46+9i; observed in native Calc: -46+9.00000000000001i. The 0.00000000000001 difference is numerical rounding, not a distinct algebraic answer.

Use a fractional exponent to find a principal square root:

=IMPOWER(A3;0.5)

Expected / observed: 2+i, because (2+i)² = 3+4i. Compare with the separate IMSQRT guide.

Use a negative power for a reciprocal:

=IMPOWER(A3;-1)

Expected / observed: 0.12-0.16i, since 1/(3+4i) = (3-4i)/25.

When source data are numeric components:

=IMPOWER(COMPLEX(B2;C2);D2)

Expected / observed: -7+24i with (B2,C2,D2)=(3,4,2). A suffix j also works: =IMPOWER("2+3j";2) returned -5+12j.

• Invalid complex text: =IMPOWER("wrong";2) produced Err:502 (native Calc error code 502). Confirm signs, numeric components and the imaginary suffix. For imported data, a text label is not a valid complex number.
• Exponent is not numeric: =IMPOWER("2+3i";"wrong") produced #VALUE! (Calc error code 519), different from the malformed-base error above. Use a numeric cell/expression for the second argument.
• Zero to negative power: =IMPOWER(0;-1) produced Err:502, consistent with division by zero. Reject or flag zero bases before negative exponents.
• Precision: Complex power uses floating-point calculations, and the cube example shows tiny text differences. Compare real/imaginary components numerically with a tolerance; do not require exact string equality.
• POWER vs. IMPOWER: ordinary POWER is for real number calculations; IMPOWER handles complex bases and returns complex text, even for a real final result. IMREAL can extract a numeric real coefficient when appropriate.
• Different signs or phases: Fractional complex powers involve a choice of branch. The observed square root is the principal result; do not assume your expected alternate root will be returned by changing a decimal format.

The current official Microsoft Excel IMPOWER reference also accepts a complex-number string plus a numeric exponent; its syntax is IMPOWER(inumber, number) in English Excel. Its documentation explicitly allows fractional and negative exponents. Excel was not executed here. The exact text serialization and rounding may differ after workbook import.

Related guides: COMPLEX · IMSQRT · IMPRODUCT · IMDIV · IMREAL · IMEXP · POWER

Official references, accessed 2026-10-11:

1. LibreOffice 26.8 Help — IMPOWER, confirms function meaning, argument order and =IMPOWER("2+3i";2) example.
2. LibreOffice Add-in Analysis Functions, confirms category and complex-number format.
3. Microsoft Excel IMPOWER, used solely for cross-compatibility.
4. Original generic Calc Help, retained from source metadata.

Selected example formulas were run in LibreOffice Calc 25.2.3.2 on Linux on October 12, 2026. The official Help may cover a newer version. Tests of selected formulas do not certify every locale, interactive array operation or file round trip. View the example-check record.

Official IMPOWER reference · Editorial standards