IMPOWER in Collabora Office: Verify Complex Integer Powers and Reciprocals

• Introduced: the original Collabora release and launch date are not established by the reviewed sources.
• Availability: documented in Collabora Office 26.04 desktop help.
• Platform scope: online and mobile deployment support is not inferred from the desktop documentation.
• Checked: October 14, 2026. Function-specific documentation and independent controls; no native Collabora execution.

=IMPOWER("ComplexNumber"; Number)

ComplexNumber uses the documented x+yi or x+yj form; Number is the exponent. The dedicated section supplies a square example but does not state a complete branch convention for fractional exponents or a full error/coercion table.

This guide uses nonzero complex bases and explicit integer exponents. Positive integer powers can be checked by repeated multiplication. Negative integer powers can be checked against reciprocals. These independently derived controls avoid assigning an undocumented fractional-power branch.

Enter the exact ASCII text 2+3j in A2. Enter exponents 1, 2, 3 and 4 in B2:B5. Put =IMPOWER($A$2;B2) in C2 and fill down. The absolute reference keeps the same complex base.

The final two columns are explanatory component checks. Put =IMREAL(C2) in D2 and =IMAGINARY(C2) in E2, then fill down to inspect them.

For the square, (2+3j)²=4+12j+9j²=−5+12j because j²=−1. Squaring the two numeric coefficients separately would give 4+9j and omit both the negative real contribution and the cross term.

Compare the exponent-two output with =IMPRODUCT(A2;A2). For the exponent-three output use =IMPRODUCT(A2;A2;A2).

The exponent-four result can also be checked with =IMPRODUCT(C3;C3), because C3 contains the square. Squaring −5+12j gives real coefficient 25−144=−119 and imaginary coefficient −120.

IMPRODUCT performs the complex multiplication. Ordinary numeric POWER applied independently to each coefficient is not a replacement for this operation.

The source’s i-suffix control and this j-suffix fixture express the same imaginary-unit arithmetic; the dedicated IMPOWER definition explicitly permits both forms. Each worked expression keeps its own suffix consistent.

For the nonzero base 2+3j, =IMPOWER(A2;-1) has independently expected coefficients 2/13 and −3/13, approximately 0.153846154 and −0.230769231.

Compare it with an explicitly constructed complex numerator:

=IMDIV(COMPLEX(1;0;"j");A2)

The denominator’s squared magnitude is 2²+3²=13. Multiplying either independently modeled reciprocal by 2+3j gives real coefficient one and imaginary coefficient zero.

IMCONJUGATE alone returns 2−3j. That is the reciprocal numerator, not the full reciprocal: it must be divided by thirteen. Keep the squared-magnitude factor visible when checking this identity.

The magnitude of the original base is sqrt(13), approximately 3.605551275. For exponents one through four, the independently expected magnitudes are sqrt(13), 13, 13×sqrt(13) and 169.

Numerically these are approximately 3.605551275, 13, 46.872166581 and 169. Use =IMABS(C2) filled down and compare with powers of the original magnitude. Do not interpret these positive magnitudes as the real coefficients of C.

For an integer exponent-addition check, =IMPRODUCT(C3;C4) multiplies the square and cube. Its independently expected quantity is the fifth power, 122-597j. This checks 2+3=5 at the exponent level using complete complex quantities.

The squared magnitude of that fifth-power quantity is 371293, equal to 13^5. A component-level and magnitude-level check together can reveal mistakes that one scalar check alone would miss.

For a noninteger exponent, multiple complex roots and a chosen branch become relevant. The reviewed section does not settle that global convention. This guide does not infer a native result for a square root on a branch boundary, zero to zero, zero to a negative power or malformed input.

The negative-exponent example is an independently derived nonzero-base control, not native error or precision certification. For approximate reproduction, compare numeric components with a stated tolerance rather than relying on exact character equality of formatted complex outputs.

• Collabora Office 26.04: IMPOWER.
• Editorial testing standards.

Complete dedicated function section reviewed. Results are independently calculated mathematical controls or explicit published examples, not captured native application results. Formulas use English names and semicolon separators.