IMLOG10: Complex Base-10 Logarithm in WPS Spreadsheet

=IMLOG10(inumber)

The one required argument is the complex number whose logarithm is wanted. The official lesson describes complex text using x+yi or x+yj; a cell can contain that input and be passed by reference. A quoted complex literal is text notation for a number, not a worksheet expression that multiplies a variable named i.

The lesson does not specify a logarithm branch or the exact zero-input error. The controls cover conventional real-logarithm values on positive real inputs and a bounded first-quadrant example corroborated by the vendor walkthrough. Wider complex branch behavior remains unverified, including the negative real axis and branch cuts.

For a positive real input r, the real coefficient is ln(r)/ln(10) and the imaginary coefficient is zero. The official formula image expresses this base change as multiplication of the complex natural logarithm by log_10(e), equivalently division by ln(10).

In general mathematical notation, a logarithm of a nonzero complex number relates magnitude and phase. Phase is not unique without a branch convention. That mathematical fact explains why a positive-real control cannot certify WPS branch choices for other inputs. No principal-branch claim is inferred from another spreadsheet.

Enter the quoted literals exactly as shown. For the cell-reference formula, place text 100+0i in A2 first. The table gives independently computed mathematical coefficients. It does not predict whether WPS serializes a real result as text, omits a zero imaginary term or chooses a particular number of displayed digits.

For =IMLOG10("3+4i"), the magnitude is sqrt(3²+4²)=5. The first-quadrant angle is atan(4/3), approximately 0.927295218002 radians. The natural-log coefficients are ln(5) and that angle. Divide both coefficients by ln(10) for this logarithm base. The independently expected coefficients are 0.698970004336 real and 0.402719196273 imaginary.

The official lesson’s published walkthrough shows input 1+3i with displayed coefficients 0.5 and 0.542453686597147. Independent magnitude-and-angle arithmetic reproduces that published example. This corroborates the bounded first-quadrant convention used here; it is vendor demonstration evidence, not a calculation performed in WPS for this guide. It does not settle full-plane branch behavior or guarantee the serialization of a new result.

Powers of ten make especially clear controls: 10 has logarithm 1 and 100 has logarithm 2. The value 0.01 is 10 to the power −2, so its result is −2. A negative logarithm here comes from a positive input below one; it does not exercise a negative-input complex branch.

For a positive ratio of 1000, the independently calculated base-10 logarithm is 3. Multiplying that ratio by another factor of 10 adds one to its base-10 logarithm. This describes powers-of-ten scaling; it does not turn the result into a particular physical unit or a decibel value without a separately defined model and multiplier.

Keep the imaginary suffix consistent within a complex-data model and use the notation documented by WPS. The lesson mentions i and j forms but does not establish every accepted spelling, embedded-space convention, uppercase suffix or text coercion rule. These controls avoid those ambiguities.

Zero has no finite complex logarithm mathematically, but the exact WPS error representation is not established by the lesson. Malformed complex text, empty cells, propagated errors, overflow and extreme magnitudes likewise have no execution-backed error table here.

For ordinary positive real calculations, the real logarithm functions may express the intent more directly. The complex function remains useful when maintaining a consistent complex-text workflow, but its name is not an exact alias for a real-only function. Any wider complex-domain use needs an independently established branch contract for the target WPS environment.

The official WPS lesson is dated 2019-06-24 and explicitly labels its applicability WPS Office for Windows Personal. It does not identify a numeric release. This establishes documentation by that date, not the function’s original introduction or its last working version. Current build limits and equivalence across WPS clients remain unverified. The available evidence does not establish retirement or formal deprecation.

Checked October 18, 2026. The examples in this guide are original, independently calculated controls based on the lesson. They have not been run in WPS or another spreadsheet application. No screenshot or execution result is claimed.

LN, LOG, LOG10.