IMREAL in Google Sheets: Extract Real Coefficients from Complex Data

• 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 IMREAL reference. Documentation and independent models, with no native Sheets execution or wider client certification.

=IMREAL(complex_number)

Google documents complex text in a+bi or a+bj form. Its explicit examples include an ordinary mixed value and the purely imaginary string 4j. COMPLEX constructs a complex value when the two coefficients already occupy numeric cells.

The returned real coefficient is an ordinary signed number. It is not the magnitude of the complex value, and zero does not imply that the entire value is zero. A nonzero imaginary coefficient may still be present.

The dedicated reference does not provide a complete parsing or error table. These examples use clear complex text and constructed values, without assigning behavior to arbitrary whitespace, uppercase suffixes or malformed imports.

Enter only the first column as Plain text in A2:A5. In B2 use =IMREAL(A2) and fill down.

The real total =SUM(B2:B5) is five. The second record contributes negative three rather than positive three; IMREAL preserves the sign of the coordinate.

For a separate documented j-notation control, =IMREAL("4j") returns zero. This is a valid pure-imaginary value, not a missing record. Preserve the original source beside the extracted column when the full quantity may be needed later.

Enter real coefficients 2, −3 and 6 in D2:D4, and imaginary coefficients 5, 4 and −2 in E2:E4. In F2 use =COMPLEX(D2,E2) and fill down.

Expected constructed quantities are 2+5i, −3+4i and 6−2i. Applying =IMREAL(F2) and filling down returns 2, −3 and 6, matching the original numeric input column.

This workflow avoids manually deciding where a plus or minus character belongs in a concatenated string. It also separates data entry from the complex representation and makes each numeric component independently inspectable.

For the first fixture, put =IMAGINARY(A2) in C2 and fill down. Expected imaginary coefficients are 5, 4, −2 and 4.

In G2 enter =COMPLEX(B2,C2) and fill through G5. The reconstructed quantities match the originals. A result representing 4i need not retain the original explicit zero real term.

Check =IMREAL(G2)=B2 and =IMAGINARY(G2)=C2, filling down. Each comparison is TRUE for these exact small values. IMAGINARY provides the coordinate that IMREAL alone discards.

A quantity-level reconstruction is different from reproducing the original text character for character. If an external file requires a particular written form, keep that text separately.

Google’s IMSUM reference explicitly supports ranges. For A2:A5, =IMSUM(A2:A5) has expected quantity 5+11i. Its real coefficient is five, matching =SUM(B2:B5).

For a weighted combination of the first two records, =3*IMREAL(A2)+2*IMREAL(A3) gives zero. The corresponding complete weighted quantity has imaginary coefficient 3×5+2×4=23, so it is not the zero complex value.

A zero real total can therefore conceal a substantial imaginary component. Label the result Real total rather than Complete total if the other coordinate is not shown.

For 2+5i multiplied by 3−i, the real coefficient is 2×3−5×(−1)=11 and the imaginary coefficient is 2×(−1)+5×3=13.

=IMREAL(IMPRODUCT("2+5i","3-i")) has expected result eleven. Multiplying only the separate real coefficients gives six, which omits the interaction between the imaginary terms.

IMPRODUCT uses the complete complex multiplication equation. Extracting real parts before the multiplication is generally not equivalent to extracting the real part afterward.

Both 2+5i and 2−5i have real coefficient two. Their imaginary coefficients differ, although both magnitudes are the square root of 29, approximately 5.385164807.

IMABS measures that magnitude. IMREAL gives a signed coordinate. Neither one scalar alone preserves the complete complex value, so choose the result according to the question being answered.

The reference does not establish every real-numeric coercion, blank input or error-code detail for IMREAL. Do not import such rules from another complex function merely because its example accepts a different input type. All outputs here are independently calculated, with no native Sheets execution.

• Google IMREAL 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.