IMPRODUCT in Collabora Office: Multiply Complex Ranges and Verify Cross-Terms

• 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.

=IMPRODUCT(Complex1 [; Complex2 [; ... [; Complex255]]])

Collabora explicitly allows complex values, cell references and cell ranges of complex numbers. The first argument is required; the nested optional syntax extends to 255 arguments.

The reference’s direct control multiplies 3+4j by 5−3j to obtain 27+11j. For a+bj times c+dj, the real coefficient is ac−bd and the imaginary coefficient is ad+bc.

The minus sign follows from j²=−1. Multiplying corresponding coefficients independently would be a different operation. These examples use explicit complex inputs rather than assuming a plain numeric scalar’s coercion rule.

Enter only the first two text columns in A1:B5. In C2 use =IMPRODUCT(A2;B2) and fill down. Expected quantities occupy the last column.

For the second row, the real coefficient is 3×1−2×(−4)=11; the imaginary coefficient is 3×(−4)+2×1=−10.

The last product has real coefficient two and imaginary coefficient zero. Its simple written quantity does not certify the native result’s storage TYPE.

For the first pair, extract coefficients a=6, b=8, c=2 and d=−1 using IMREAL and IMAGINARY.

The numeric checks are =6*2-8*(-1), giving 20, and =6*(-1)+8*2, giving 10. Constructing =COMPLEX(20;10;"j") reproduces the product quantity.

Using ac+bd instead would give 4 for the real coefficient. That plausible-looking number exposes why the cross-term sign must be checked.

Enter exact text 1+j, 2-j and 3+2j in E2:E4. Use:

=IMPRODUCT(E2:E4)

Expected quantity: 7+9j. The first two factors give 3+j; multiplying by 3+2j gives real coefficient 9−2=7 and imaginary coefficient 6+3=9.

The scalar-reference version =IMPRODUCT(E2;E3;E4) has the same independently expected quantity. Range support is explicit in this product’s source; no blank or mixed-type aggregation policy is inferred from it.

A single-input call retains the input quantity under the formal syntax. It does not square that input automatically.

To double 6+8j without relying on undocumented numeric coercion, use the explicit complex factor 2+0j. =IMPRODUCT("6+8j";"2+0j") has expected quantity 12+16j.

Multiplying by 0+1j instead produces −8+6j. Repeating the quarter-turn gives −6−8j, then 8−6j, then the original 6+8j. Every state has magnitude ten.

COMPLEX can build those explicit factors from numeric coefficients with a supplied “j” suffix.

Multiplying 6+8j by its conjugate 6−8j yields real coefficient 100 and imaginary coefficient 0. IMCONJUGATE provides that sign reversal.

For the first paired product, =IMDIV(C2;B2) recovers 6+8j, since B2 is nonzero. IMDIV reverses the multiplication under its own numerator/denominator contract.

The product magnitude is the square root of 500, approximately 22.360679775. It equals ten times the square root of five mathematically, offering another independent check.

All range cells here contain valid, consistently suffixed complex text. The 255-argument statement does not specify every range-size, blank, ordinary-text or error policy.

Native malformed-input errors, mixed-suffix handling, zero coercion and extreme overflow remain unverified. Component calculations and moderate exact fixtures are the verification scope, not a promise of identical last digits under every evaluation order.

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

Complete function-specific documentation reviewed. Outputs are independent complex-component models or explicit documented controls, not captured native application results. Formulas use English names and semicolon separators; optional-argument brackets describe syntax and are not typed into working formulas.