IMLOG2 in Collabora Office: Track Binary Scaling of Complex Quantities

• 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.

=IMLOG2("ComplexNumber")

The dedicated Collabora section accepts the documented x+yi or x+yj complex form and identifies a binary logarithm. This is a logarithm with base two, not a conversion of a decimal quantity into a string of zero and one digits.

For the first-quadrant inputs here, the independent formula is the natural complex logarithm divided by ln(2). Its real coefficient measures log2 of the magnitude; its imaginary coefficient is the first-quadrant angle divided by ln(2).

The source does not establish a global argument interval or negative-axis branch convention. The examples retain positive real and imaginary coefficients.

Format A2:A5 as Text and enter 1+j, 2+2j, 4+4j and 8+8j. Put =IMLOG2(A2) in B2 and extract real and imaginary coefficients in C2:D2 with IMREAL and IMAGINARY. Fill down.

The input magnitudes are sqrt(2), twice sqrt(2), four times sqrt(2) and eight times sqrt(2). Since sqrt(2)=2^0.5, the real coefficients increase from 0.5 in steps of one.

The imaginary value is pi/(4×ln(2)), shown to nine decimals. It stays constant because all four inputs point in the same first-quadrant direction.

For =IMLOG2("3+4j"), the independently expected coefficients are 2.321928095 and 1.337804212. For 4+3j, they are 2.321928095 and 0.928375858.

Both inputs have magnitude five, so log2(5) appears in both real parts. Their imaginary parts distinguish their directions. A scalar log2 magnitude therefore cannot substitute for the complete complex result.

=LOG(IMABS("3+4j");2) supplies the real magnitude summary explicitly. The base argument of LOG is two; the imaginary coefficient remains information that this real formula does not return.

For each primary input, compare the IMLOG2 output with:

=IMDIV(IMLN(A2);COMPLEX(LN(2);0;"j"))

This has the same expected coefficients as the table. The real complex divisor is constructed explicitly, so no undocumented acceptance of a plain numeric argument by IMDIV is needed.

For 1+j, the natural-log real part ln(2)/2 becomes exactly 0.5 in the mathematical model. The angle pi/4 becomes approximately 1.133090035 after division by ln(2). It has changed units as a logarithm coefficient; interpreting it directly as the original angle would be wrong.

IMLN supplies the natural complex logarithm, and IMDIV divides the complete quantity.

Put =IMSUB(B3;B2) in F2, =IMSUB(B4;B3) in F3 and =IMSUB(B5;B4) in F4. Each independently expected difference has real coefficient one and imaginary coefficient zero.

The total difference between the last and first logarithms is three, representing three doublings. The corresponding positive-real scale factor is 2^3=8; this agrees with the original coefficient change from 1 to 8.

To reconstruct an original quantity from B2, use:

=IMEXP(IMPRODUCT(B2;COMPLEX(LN(2);0;"j")))

Filled down, the expected quantities are 1+j, 2+2j, 4+4j and 8+8j. Use both IMREAL and IMAGINARY comparisons against the original values, with a stated tolerance such as 1e-9 for this fixture. Keep unrounded formulas rather than retyping the displayed coefficients.

Zero has no finite logarithm, but the reviewed source does not establish its native error code. Negative-axis representatives, malformed complex text, mixed suffixes and numerical overflow or underflow are also not certified here.

Do not confuse a change of one in this logarithm with adding one to the original complex number. It corresponds to multiplying the entire quantity by two in the positive-real scaling examples. General complex product identities require branch awareness; these controlled doublings do not establish an unrestricted identity across every quadrant.

• Collabora Office 26.04: IMLOG2.
• 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.