IMABS 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.

IMABS returns the magnitude of a parsed complex number. For a+bi it is √(a²+b²), a nonnegative real number. It is not the sum of the components and it does not preserve the complex number’s phase. Release entry.

=IMABS(ComplexNumber)

One complex-number argument is required. The add-in accepts a string using its parser’s grammar, including lowercase i or j. A pure real string and pure imaginary strings are also meaningful. Invalid strings raise an argument error rather than silently becoming zero.

The native column records the saved 4.1.16 results. Ordinary numeric values are rounded to twelve decimal places, with scientific notation for tiny values. Stored values and display text were inspected separately; a twelve-decimal cell display can hide a tiny nonzero number.

=IMABS("3+4i") gives 5. The values 3−4i, −3+4i and −3−4i also have magnitude 5. Squaring the components removes their signs, so magnitude alone cannot identify the quadrant.

When real and imaginary measurements are stored separately, construct the value explicitly with COMPLEX. For A2=3 and B2=4, the independent composition =IMABS(COMPLEX(A2;B2)) corresponds to SQRT(3²+4²)=5. The literal cases in the table are the directly tested formulas.

For complex values z and w, |zw|=|z||w| and, for w≠0, |z/w|=|z|/|w|. Addition instead obeys the triangle inequality |z+w|≤|z|+|w| and can exhibit cancellation. For example, 3+4i and −3−4i each have magnitude 5 but sum to zero.

A number and its conjugate have the same magnitude. Their product is the real value |z|², so (3+4i)(3−4i)=25. These provide independent mathematical checks without assigning a probability interpretation to the magnitude.

For physical models, magnitude retains the units of the components. Real and imaginary components must be quantities that can meaningfully form one complex value; the worksheet function does not supply that modeling assumption.

The zero complex number has magnitude zero and is valid here. That does not make its phase well-defined; IMARGUMENT has a different zero-input rule.

Invalid text and an empty string must not be assumed equivalent to a deliberate zero. The exact observed errors and numeric-argument conversion are recorded below. Very large or tiny components can stress finite-precision arithmetic beyond this ordinary reference set.

These additional formulas were recalculated through the same import path. Error displays are retained as errors, even when an ODS numeric attribute stores zero.

The IMABS 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
• Numeric algorithm or complex parser/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.