IMARGUMENT Function (Calligra Sheets)

• Introduced: First release not established; the name is present in Calligra 2.4.0 source.
• Supported in: Calligra Sheets 26.08.2, with no retirement established.
• Scope: Desktop Sheets with the Engineering module. Examples use English semicolon-separated formulas.
• Checked: October 14, 2026. Formulas were executed through the official 25.04.2 engine library and checked against source and independent mathematics. This is not GUI-cell or workbook-import evidence; 26.08.2 was source-checked, not executed.

IMARGUMENT returns the phase angle of a complex value a+b·i. For a nonzero value, the angle is determined by both components, like atan2(b,a), rather than by ATAN(b/a) alone. The result is numeric radians; quadrant information is essential when the real component is negative. Function help.

=IMARGUMENT(complexValue)

Exactly one argument is required. Use a native COMPLEX value or a tested complex text representation. The implementation delegates to the standard complex argument operation. A positive real value has angle 0; the tested real value −1 has angle π. Values on a branch boundary can be sensitive to signed zero. Registration and implementation, with versioned help.

Noninteger results are rounded to twelve decimal places. The formulas construct the input components explicitly, making each case reproducible.

With 3 in A2 and 4 in B2, =IMARGUMENT(COMPLEX(A2;B2)) gives about 0.927295218002 radians. The recorded =IMARGUMENT(COMPLEX(3;4))*180/PI() gives about 53.130102354156 degrees. State the unit in the result column; formatting a radian value does not convert it to degrees.

Compare 3+4i with −3+4i. Their magnitudes are both 5, but their phases are about 0.927295218002 and 2.214297435588 radians. The second lies in the upper-left quadrant. A plain ratio b/a loses the information needed to distinguish those directions.

At the origin the phase is mathematically undefined, even though the tested IMARGUMENT(COMPLEX(0;0)) returns 0. Treat that as an implementation result, not an observed direction. In an analysis sheet, test the magnitude against an appropriate model-specific threshold before interpreting the phase.

Two versioned-help examples disagree with the inspected implementation and the engine tests: IMARGUMENT("1.2+5i") gives about 1.335251346074, and IMARGUMENT("12") gives 0, rather than the help’s listed 0.6072 and division error. The current function returns a numeric angle despite the help’s string-type label.

Invalid text “abc” and empty text also returned 0 because the shared complex converter substitutes zero on failed parsing. Validate source text separately; an angle of zero cannot distinguish a valid positive real input from those failures. A missing argument returned #VALUE!.

The complex conversion helper explains the text and Boolean cases above. The inspected Engineering module and complex converter are byte-identical between 25.04.2 and 26.08.2. That source comparison does not establish every locale, import path or extreme-value case.