IMLN 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.

IMLN returns the principal natural logarithm of a nonzero complex value. Its real component is LN(|z|), and its imaginary component is the selected principal phase in radians. Negative real values therefore have valid complex logarithms. Function help.

=IMLN(complexValue)

Exactly one argument is required. A numeric real input is accepted as a complex value with zero imaginary component. COMPLEX makes the intended components explicit in the examples. Registration and implementation, with versioned help.

Results are shown as (real,imaginary) component pairs, rounded to twelve decimal places, not a literal cell format. A component rounded to zero is shown as 0; the stored value may still contain a tiny residual or signed zero. NaN means not-a-number; infinity and NaN are not finite results.

=IMLN(COMPLEX(3;4)) gives approximately 1.609437912434+0.927295218002i. The magnitude of 3+4i is 5, so the real component is LN(5); the imaginary component is atan2(4,3). Taking LN(3) and LN(4) separately would not calculate this function.

For a positive real input 1, the result is zero. For the explicitly constructed −1+0i input, the engine returned imaginary component π with zero real component. The sign or approached side of the negative real axis matters when reasoning about a principal branch.

A principal logarithm does not invert every complex exponential without adjustment. The executed =IMLN(IMEXP(COMPLEX(0;4))) returned imaginary component approximately −2.283185307180, equal to 4−2π, and a negligible real residual around −2.63E-20. The original imaginary input 4 lies beyond the selected principal phase interval.

Likewise, LN(z×w)=LN(z)+LN(w) may require an integer multiple of 2πi to reconcile branch choices. For z=w=−1, the product is 1 with principal logarithm zero, while the two individual principal logs add to 2πi. Do not apply real-log identities blindly to complex phases.

The zero-input engine result was (−Infinity,0) with no engine error flag. Zero has no finite complex logarithm. Invalid text and an empty string were first converted to zero and produced the same nonfinite components. These observations do not establish a GUI-cell error label.

TRUE became 1 and returned zero. Zero arguments and two arguments produced #VALUE!. Check the original input and its nonzero magnitude; a false engine error flag alone does not guarantee a finite or meaningful logarithm.

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.

Use COMPLEX to construct values from numeric components, IMABS for magnitude, and IMARGUMENT for principal phase.