PlanMaker IMLOG10: Use complex base-ten logs without losing angle units
IMLOG10 returns the base-ten logarithm of a complex number. For these first-quadrant and positive-real inputs, divide the natural complex logarithm by ln(10). Both coefficients are scaled; the returned imaginary coefficient is not directly an angle in radians.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
IMLOG10 returns the base-ten logarithm of a complex number. For these first-quadrant and positive-real inputs, divide the natural complex logarithm by ln(10). Both coefficients are scaled; the returned imaginary coefficient is not directly an angle in radians.
Availability and evidence
The PlanMaker 2026 reference, 2024 reference and 2021 reference were retrieved and read on October 15, 2026. They establish documented support in those manual families, not the original introduction or a last-working-version endpoint. Both historical endpoints remain unverified; specific FreeOffice/mobile editions and every desktop build are outside the checked scope.
No native PlanMaker execution, screenshot or workbook export was performed. Numerical expectations are independent mathematical calculations. English formulas use commas between arguments; check localized names and separators in the installed build.
Exact syntax and arguments
=IMLOG10(ComplexNumber)
One complex argument is required. The base is fixed at 10; there is no optional base argument. A full branch convention, zero-input error and negative-axis endpoint behavior are not specified in the short reference.
Represent and inspect the result
The documented inputs are complex numbers written in x+yi or x+yj form. A literal such as "2+4i" needs quotation marks in a formula. The COMPLEX reference supplies a safer construction method when real and imaginary coefficients occupy separate numeric cells. Its default suffix is lowercase i; lowercase j is an alternative.
The worksheets use COMPLEX with its default i suffix. They compare the returned value through IMREAL and IMAGINARY, rather than requiring an exact text spelling, spacing or number of trailing zeroes. A zero imaginary coefficient might be displayed more simply by the application; a mathematically real result is still a valid outcome of a complex calculation. Mixed i/j inputs and parser variants are outside the verified scope.
Complete coefficient worksheet
Create ComplexValues with real coefficient in A and imaginary coefficient in B. Use C2 =COMPLEX(A2,B2) and D2 =IMLOG10(C2). Inspect E2 =IMREAL(D2) and F2 =IMAGINARY(D2). Fill through row 7.
| Row | A | B | Expected E | Expected F |
|---|---|---|---|---|
| 2 | 1 | 0 | 0.000000000 | 0.000000000 |
| 3 | 2 | 0 | 0.301029996 | 0.000000000 |
| 4 | 2 | 4 | 0.650514998 | 0.480828579 |
| 5 | 3 | 4 | 0.698970004 | 0.402719196 |
| 6 | 1 | 1 | 0.150514998 | 0.341094088 |
| 7 | 5 | 12 | 1.113943352 | 0.510732572 |
Enter the numeric coefficient columns exactly as shown. Expected components are rounded to nine decimal places for comparison; they are not observed native strings or a promised implementation precision.
Check the documented coefficients
For 2+4i, SoftMaker shows approximately 0.650514997831991+0.480828578784234i. The real coefficient is log10(√20). The imaginary coefficient is arctan(2)/ln(10). Multiplying only the imaginary result by ln(10) recovers the first-quadrant angle in radians.
For 3+4i, the magnitude is 5 and the real coefficient is log10(5), approximately 0.698970004. In a copy change A5:B5 to 30,40. The magnitude grows to 50, so the real coefficient becomes 1.698970004. The imaginary coefficient stays approximately 0.402719196 because positive scaling does not rotate the input.
Advanced: make a relative amplitude display
Suppose a supplied dimensionless complex amplitude ratio is 3+4i. Put =COMPLEX(3,4) in F2, =IMLOG10(F2) in G2 and =20*IMREAL(G2) in H2. The expected H2 value is approximately 13.979400087 under the explicitly chosen 20log10(amplitude-ratio) convention.
This is not the same convention as 10log10(power-ratio). The workbook must define the measured quantity and reference first. The function does not decide whether an amplitude, power or other physical convention fits the data. Keep any units and reference measurement outside the conversion formula.
In a copy replace F2 with =COMPLEX(6,8). The magnitude doubles from 5 to 10, H2 becomes 20, and the difference is approximately 6.020599913. Doubling the two coefficients together changes amplitude while retaining the same angle.
Advanced: recover magnitude and direction separately
On the original sheet =POWER(10,IMREAL(G2)) reconstructs magnitude 5. =IMAGINARY(G2)*LN(10) reconstructs the first-quadrant direction, approximately 0.927295218 radians. Interpreting IMAGINARY(G2) itself as radians would give the wrong angle.
As another check, subtract IMLOG10(COMPLEX(3,4)) from IMLOG10(COMPLEX(30,40)) with IMSUB. The expected coefficient pair is (1,0): one decade of scale and no phase change. These controls stay away from negative-axis branch boundaries and do not establish a universal logarithm-of-product identity over every complex input.
Troubleshooting and verification limits
Check the input coefficients, argument order and actual formulas before changing display precision. A quoted cell address is text, not the referenced cell. Keep complex construction and coefficient inspection separate from ordinary text concatenation.
The short reference does not specify every coercion, mixed-suffix, blank, array, extreme-value or malformed-input error case. Do not import an error token or parser behavior from another spreadsheet. Record the exact PlanMaker build, edition, platform, language and file format before native testing. Recreate the original fixture, apply each changed-input control to a copy, then verify save/reopen and any destination format separately.