IMSUM Function (OpenOffice Calc)

• Introduced: First release not established; documented by OpenOffice.org 3.3.
• Supported in: Apache OpenOffice 4.1.16; this identifies a verified release, not a final supported version.
• Scope: Desktop Calc with its Analysis add-in, English function names and semicolon-separated formulas.
• Checked: October 14, 2026. Eight reference formulas and the listed diagnostics were recalculated after XLSX import in 4.1.16 on Linux x86-64, Build 9816. Source and independent reference calculations were also checked.

IMSUM adds complex numbers and returns a complex-number string. It adds real parts to real parts and imaginary parts to imaginary parts. It does not add magnitudes, and an ordinary SUM formula is not a substitute for adding cells that contain complex-number text. Release entry.

=IMSUM(ComplexNumber1 [; ComplexNumber2; …])

Supply a first complex value or range, with further values or ranges as needed. The add-in collects values into a complex list and skips empty entries. A nonempty malformed string is rejected. Real numeric values contribute to the real component; lowercase i and j are recognized imaginary-unit suffixes.

The native column records the saved 4.1.16 results. The native strings are retained exactly. Independent component references are rounded to twelve decimal places, with rounded negative zero shown as zero. A tiny stored residual can therefore appear in the native string beside a reference component rounded to zero. Every successful result below is string-typed, including pure real-looking outputs.

Two phasors represented by 3+4i and 1−2i sum to 4+2i. The tested formula is =IMSUM("3+4i";"1-2i"). This component-wise sum differs from adding the magnitudes 5 and √5. Retain the original components when checking cancellation or phase.

For a worksheet, put the two validated complex strings in A2:A3 and use =IMSUM(A2:A3). That range layout follows the inspected collection contract; the table directly tests literal arguments rather than this additional range formula. Keep the same physical units and reference phase for quantities that you add.

For z=a+bi and w=c+di, z+w=(a+c)+(b+d)i. Opposite values cancel: (3+4i)+(−3−4i)=0 even though each has magnitude 5. Addition is mathematically commutative and associative, but floating-point summation can lose small contributions when the scales differ greatly.

The triangle inequality gives |z+w|≤|z|+|w|. Equality is not automatic. In the first example, |4+2i|=√20≈4.472135955, while the sum of the input magnitudes is about 7.236067977. These independent checks help detect accidental magnitude addition.

The result is formatted text. A pure real output such as 3 remains the result of the complex-string function; use an appropriate IM function for subsequent complex arithmetic.

An empty entry is skipped by this function, but a nonempty invalid string is an error. When the collected list contains no values, the implementation returns the string 0. This is a specific collection rule, not evidence that every complex function treats an empty string as zero.

The diagnostics distinguish an explicit empty string, a deliberately empty H5 reference and invalid text. Mixed i/j suffix choices and unusual imported text should be validated before calculation; the examples establish the listed forms only.

These additional formulas were recalculated through the same import path. H5 is a deliberately empty cell where referenced. Error displays are retained as errors, even when an ODS numeric attribute stores zero.

The IMSUM guide for Calligra Sheets documents that product’s own syntax and tested behavior. A shared function name does not guarantee the same argument conversion, text parsing, branch or precision rules.

• Function-specific release entry
• Complex algorithm or collection helper
• Strict complex-string parser
• Finite-output string formatter

The saved ODS retained every tested formula identity. A deliberately stale SUM cache changed from 999999 to 3, and an uncached SUM returned 7 after hard recalculation. Native evidence covers the eight reference formulas and listed diagnostics only. Other explanatory compositions are independent mathematical checks; other releases, locales and extreme-value behavior were not established by this run.