IMLOG10 in Collabora Office: Measure Complex Decades Without Losing Direction

• 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.

=IMLOG10("ComplexNumber")

The documented complex forms use x+yi or x+yj. The dedicated section identifies a common logarithm and supplies one first-quadrant example. It does not give a complete branch interval, coercion table or native error policy.

For this guide’s first-quadrant values, the independent model divides both coefficients of the natural complex logarithm by ln(10). The real coefficient is log10 of the magnitude. The imaginary coefficient is the first-quadrant angle divided by ln(10); it is not simply an angle displayed in degrees.

Format A2:A5 as Text and enter 1+j, 3+4j, 30+40j and 300+400j. Put =IMLOG10(A2) in B2. Calculate C2 with =IMREAL(B2) and D2 with =IMAGINARY(B2), then fill down.

These are independent coefficients rounded to nine decimals, not prescribed native output strings. Retain the original formulas for subsequent calculations.

The last three magnitudes are five, fifty and five hundred. Every multiplication by ten adds one to the logarithm’s real coefficient. Their direction is unchanged, so their imaginary coefficients match.

Put =LOG10(IMABS(A2)) in E2 and fill down. The expected results equal C2:C5. LOG10 receives the real magnitudes from IMABS.

For 4+3j, the magnitude is also five, and its real logarithm remains 0.698970004. Its complex logarithm has a different imaginary coefficient, approximately 0.279468981. The radial summary cannot distinguish it from 3+4j.

The full complex function preserves more information than applying an ordinary logarithm to a displayed string or keeping only the magnitude.

For each input, compare B2 with:

=IMDIV(IMLN(A2);COMPLEX(LN(10);0;"j"))

The independently expected real and imaginary coefficients are those in the primary table. The explicit COMPLEX construction supplies a nonzero real divisor in complex form, avoiding an assumed numeric-coercion contract.

Both coefficients are divided by ln(10). Dividing only the real part would leave the imaginary coefficient incorrectly scaled. For the source input 1+j, pi/(4×ln(10)) is approximately 0.341094088, rather than pi/4.

Use this expression in F2 and fill down:

=IMEXP(IMPRODUCT(B2;COMPLEX(LN(10);0;"j")))

Expected recovered quantities are 1+j, 3+4j, 30+40j and 300+400j. Multiplication by ln(10) first reverses the base change, then the complex exponential reconstructs the quantity.

Compare both extracted coefficients with the original input using an absolute tolerance such as 1e-8 for this modest fixture. This is an explicit numerical checking target, not a source guarantee. Do not reconstruct from the nine-decimal printed coefficients if your goal is to evaluate the unrounded formulas.

The logarithm difference =IMSUB(B4;B3) has independently expected real coefficient one and imaginary coefficient zero. It measures one decade of positive-real scaling, not a change of direction.

The first-quadrant model matches the quadrant of the official example. It does not certify the chosen representative on the negative real axis or a global principal-angle interval. No exact zero-input error code is supplied by the reviewed section.

Logarithms may differ by branch-dependent imaginary offsets; unrestricted product and power identities need that context. The worked decade scaling uses positive real factors, so no unresolved cross-axis branch choice is needed. Very large inputs, malformed representations, mixed suffixes and native precision boundaries require separate target-product verification.

• Collabora Office 26.04: IMLOG10.
• Editorial testing standards.

Complete dedicated function section reviewed. Results are independently calculated mathematical controls or explicit published examples, not captured native application results. Formulas use English names and semicolon separators.