IMSUM in Google Sheets: Add Complex Ranges and Weighted Components

• Introduced: first introduction date is not established by the reviewed official history; no desktop release number is inferred.
• Availability: documented in the rolling Google Sheets service; these examples use the web worksheet workflow.
• Checked: October 14, 2026; official IMSUM reference. Documentation and independent models, with no native Sheets execution or wider client certification.

=IMSUM(value1,[value2,...])

The first value or range is required; further values or ranges are optional. Google’s examples mix complex strings, numeric real values and ranges. The reviewed reference does not state a maximum argument count, so no limit from another spreadsheet is assumed here.

For two values, the documented rule is (a+bi)+(c+di)=(a+c)+(b+d)i. A numeric real input contributes only to the real total. Google’s explicit j example combines 20+5j, numeric four and j to obtain 24+6j.

Google says complex inputs with different i/j suffixes cannot be summed together. These fixtures use i consistently. The page does not classify the exact mixed-suffix error or every possible blank, text or error value in a range.

Enter these exact strings as Plain text in A2:A4: 2+5i, -3+4i, 6-2i. Then put the formula below in A6, outside the input range.

=IMSUM(A2:A4)

The expected quantity is 5+7i: the real total is 2−3+6=5, and the imaginary total is 5+4−2=7.

In B2 use =IMREAL(A2) and in C2 use =IMAGINARY(A2), filling both down through row four. The numeric columns are:

=SUM(B2:B4) returns five and =SUM(C2:C4) returns seven. Constructing those two totals with COMPLEX gives the same modeled quantity as IMSUM.

Use =IMSUM(A2:A4,4) in A7. The expected result is 9+7i because the real adjustment increases only the first coefficient.

Contrast that with =IMSUM(A2:A4,"4i"), which has expected result 5+11i. Numeric four and four times the imaginary unit are different inputs.

For an explicit mixed range-and-cell expression, =IMSUM(A2:A3,A4) still produces 5+7i. This uses each record once. =IMSUM(A2:A4,A4) includes the last record twice and instead gives 11+5i.

Overlapping selections are a model-level double-counting problem, not a deduplication feature. Place totals outside the referenced input region so that filling or extending the range does not accidentally include its own total.

Suppose the first record counts three times and the second counts twice. Enter:

=IMSUM(IMPRODUCT(3,A2),IMPRODUCT(2,A3))

The scaled quantities are 6+15i and −6+8i. Their sum has real coefficient zero and imaginary coefficient 23.

Separate coefficient checks are =3*B2+2*B3, which gives zero, and =3*C2+2*C3, which gives 23. IMPRODUCT performs the complex scaling in the combined formula.

A real coefficient of zero does not mean that this weighted sum is zero. If a report shows only the real helper total, label it accordingly rather than presenting it as the entire complex quantity.

The first two records sum to −1+9i. Adding the third yields 5+7i. Grouping the last two first gives 3+2i; adding the first also yields 5+7i.

Reproduce both groupings:

=IMSUM(IMSUM(A2,A3),A4)
=IMSUM(A2,IMSUM(A3,A4))

For these exact small integers, both component models agree. Subtracting A4 from the complete sum with =IMSUB(IMSUM(A2:A4),A4) recovers −1+9i. This is a useful independent record-selection check.

The algebraic grouping identity is not a promise of identical last-bit behavior for every large, tiny or poorly scaled input. Keep a stated numeric tolerance when checking more demanding data.

The values 6+8i and 6−8i sum to a quantity with real coefficient twelve and imaginary coefficient zero. Its magnitude is twelve. Their separate magnitudes are ten each, whose sum is twenty.

Thus IMABS of an IMSUM answers a different question from adding the magnitudes. Directional cancellation can be meaningful and should not be removed by taking absolute values prematurely.

The dedicated reference supports the input forms and addition rule used here. It does not establish general treatment of noncomplex text, formula-empty cells, range errors or native storage types for real-only results. Those boundaries remain unverified; no native Sheets execution was performed.

• Google IMSUM reference.
• Editorial testing standards.

Examples use fictional data, English function names and comma separators. Expected outputs are independent mathematical calculations or explicitly documented rules, not native Sheets captures. Check the spreadsheet locale when reproducing punctuation-sensitive formulas.