Zoho Sheet IMABS: Find a Complex Number Magnitude

=IMABS(complex_number)

complex_number is the required text representation of a complex number, for example "2+3j". Zoho publishes no optional arguments, sign selector, rounding choice, or numeric-unit setting for IMABS. There is one argument, which can be supplied as a quoted example string or, for a spreadsheet workflow, by reference to a cell holding an appropriate representation. The public article shows both i and j notation across examples. It does not document every possible string grammar or numeric coercion rule.

For any mathematically valid complex number z=a+bi, its modulus is |z|=sqrt(a²+b²), always nonnegative. Thus a sign change in an imaginary coefficient can change the complex value without changing its modulus if the magnitude of that component stays the same. The mathematical formula is independently verifiable with Python’s abs(complex(a,b)), but testing a Python number is not executing the Zoho Sheet formula.

Enter A1=Complex number and B1=Magnitude. Put the following text into cells A2:A5, then enter =IMABS(A2) in B2 and copy through B5. Compare against the table. For a literal-control test, enter =IMABS("2+3j") in an empty cell and compare with the vendor’s published output.

Do not expect equal displayed decimal places in every cell; worksheet formatting may shorten a result. Compare numerical values within an appropriate tolerance. For A2, the underlying mathematical value is sqrt(13)=3.605551275463989.... For A3 it is sqrt(17)=4.123105625617661.... Zoho’s documentation rounds these values; matching the first several digits is the relevant numerical check, not matching a string with an exact number of decimal places.

In 2+3j, IMREAL supplies 2 and IMAGINARY supplies 3. IMABS supplies sqrt(13). The first two identify the position along axes; the third is the radial distance. In 1-4i, the imaginary coefficient is negative but the modulus remains positive. Do not use ABS(IMAGINARY(...)) as a replacement for IMABS unless the real component is known to be zero. For a pure imaginary input such as 5j, both happen to give 5, which makes a poor sole test case because it conceals the distinction.

Magnitude also differs from a phase angle. A complex number’s phase is conventionally derived from the angle of (a,b) and is separately documented by Zoho’s IMARGUMENT function. No phase result is produced by IMABS. A workbook calling the magnitude “angle” or “real part” introduces an interpretation error even when the calculation is numerically correct.

Suppose a two-component measurement has resistance in A2 and reactance in B2, both in the same compatible unit (e.g. ohms). In C2 construct the complex representation with =COMPLEX(A2;B2;"j"). In D2 calculate =IMABS(C2). In E2 independently compute =SQRT(A2^2+B2^2). The two results are mathematically expected to agree within numerical precision. For A2=3 and B2=4, the expected magnitude is 5. This is a useful quality-control pattern because it compares two different representations of the same mathematical quantity.

Use a second record A3=3, B3=-4. Its magnitude is also 5, but the imaginary sign is different. If the report needs direction or reactance sign, keep the components alongside the magnitude. Magnitude alone loses that information. In a signal-processing exercise, the same logic applies to real/imaginary amplitude coordinates, but the meaning of the measurement should be documented separately from formula syntax.

Normalized relative magnitude: If baseline complex text is stored in C2 and a new observation in C3, an independently reasoned formula =IMABS(C3)/IMABS(C2) gives the ratio of magnitudes when the denominator is nonzero. An important application-side guard is to verify the baseline is not zero before dividing. Zoho’s IMABS page does not establish which division-by-zero error appears in all contexts, so do not invent a specific native result. Always keep input samples and denominator controls visible for an auditable workbook.

Sanity check using components: =IMREAL(C2)^2+IMAGINARY(C2)^2 should equal =IMABS(C2)^2 mathematically. For decimal inputs, compare within a tolerance such as 1E-9 times an appropriate scale, not through strict text equality. This check depends on the related documented functions and independently derived identity, and awaits actual Zoho execution.

• #VALUE!: Zoho lists invalid argument types as possible. Inspect source strings for missing imaginary notation, unexpected whitespace or units appended to the complex representation. The source does not define its entire string parser, so precise effects of each odd input are unknown.
• #NAME!: Check spelling of IMABS, quotation marks around constant-form strings, and defined names. The error taxonomy comes from Zoho’s published help.
• #REF!: Repair incorrect, moved or deleted cell references before investigating complex arithmetic.
• #N/A!: Included in the vendor’s shared possible-error table; its exact normal trigger is not defined for valid complex values in the IMABS article.
• Surprisingly low output: Verify whether the formula accidentally uses the real or imaginary extraction function instead of magnitude. Compare 3+4i, a simple example where both components differ from the modulus.
• Negative value shown: A complex modulus cannot be negative mathematically. Inspect whether the cell actually contains IMAGINARY output, a negative sign manually added elsewhere, or a failed conversion. Do not pretend an impossible result was observed in Zoho.
• Precision and display: Cell formatting changes displayed decimal digits. Vendor help gives rounded outputs. Avoid asserting an undocumented internal precision limit; use tolerances to evaluate results.
• Cross-platform data: Import support does not ensure the same formatting or same parser treatment for all complex-number strings. Inspect a native source workbook before and after conversion.

COMPLEX assembles components; IMREAL retrieves a; IMAGINARY retrieves b. Zoho’s IMARGUMENT covers phase and is a checked external related reference; it is outside the scope of this guide.

Why is the magnitude of 1-4i positive? Because it is sqrt(1²+(-4)²)=sqrt(17), which is nonnegative.

Is IMABS("5j") enough to test whether my formula works? No. Use a nonzero real component too, such as 2+3j, to distinguish modulus from a single component.

Does IMABS change the sign or format of the input? It calculates a numeric modulus, not a rewritten complex string. How the workbook displays the decimal result depends on cell formatting.

What Zoho Sheet version supports IMABS? The checked public help does not state the earliest release or account tier. No fabricated version guarantee is included.

This is a guide to Zoho Sheet, based on its public English-language function help, retrieved on 13 October 2026. The vendor examples display semicolons between arguments. Copy the formulas exactly into an English-language Zoho Sheet worksheet using the illustrated syntax; if a workbook uses different regional or language preferences, consult the editor’s displayed function helper and its locale settings rather than silently replacing separators. Zoho documents configurable spreadsheet locale, language and calculation preferences; this guide does not infer a particular separator for every account or locale. The function article does not give a first-supported release, minimum plan, exhaustive mobile compatibility or an exact back-end engine build, so none is asserted here. The documentation establishes the function’s availability in the public Zoho Sheet reference, not execution in our account.

A formula beginning with = is an instruction for an actual spreadsheet. The expected result columns above come from Zoho’s own examples where explicitly marked, or independent mathematical evaluation where marked; none was executed in Zoho Sheet. Mathematical agreement does not prove how every string input, cell formatting choice, import conversion or edge case is handled by Zoho. This distinction matters especially for string representations of complex numbers, which should not be mistaken for a separate native complex-number cell type.

How to reproduce the examples

Create a blank sheet, enter each specified input into its designated cell and paste the formula into a different cell. Check that the input is a value rather than a string containing a leading apostrophe unless the formula specifically calls for text. Read the formula result in the cell and, if helpful, inspect the formula bar to distinguish the stored expression from what is displayed. Do not use formatted example text as proof of an exact output representation unless Zoho explicitly shows it. For comparison across regional settings, first record the workbook locale and whether the formula editor inserts semicolons. Keep a simple control case from Zoho’s own documentation in the same sheet.

Compatibility and source limits

Zoho lists .xlsx, .xls, .xlsm, .ods, .csv and other import formats in its file-format guide. File import support is not evidence that a complex-number formula will calculate identically in another spreadsheet application. When exchanging workbooks, verify the formula survived import/export, that suffix text remains lowercase where required and that outputs retain their meaning. For CSV export, remember that CSV preserves displayed values, not a working formula workbook; inspect an exported copy rather than assuming formulas survive. This guide makes no untested assertion of parity with Excel, Google Sheets, desktop apps, mobile clients, custom functions or specific subscription tiers.

References for these qualified claims: Zoho Sheet file formats and Zoho Sheet preferences and locale, both retrieved 2026-10-13.

• Authoritative function reference: Zoho Sheet IMABS help; checked 2026-10-13. This source supports the documented purpose, exact argument order, syntax, named error categories and the explicitly cited vendor examples. It does not supply a function-introduction date.
• Supporting vendor references: Zoho Sheet complex-function catalogue, locale preferences, and supported file formats; checked 2026-10-13. These support related-function names and qualified platform/locale/import statements, not precise compatibility equivalence.
• Independent validation: Standard complex arithmetic in Python (built-in complex/abs) with manually derived checks. These independent calculations are not Zoho Sheet executions.
• Outstanding review: Native confirmation of formula parsing, cell formatting, import/export conversion, unusual string forms and any account/locale-specific behaviour.