IMAGINARY in Excel: Extract Signed Imaginary Coefficients

• Introduced: the first introduction version is not established by the reviewed official history.
• Availability: official help lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Checked: October 14, 2026; official IMAGINARY reference. Documentation and independent models; no native Excel execution or wider platform certification.

=IMAGINARY(inumber)

Inumber is required. The function reads a complex value in i or j text notation. Microsoft also explicitly demonstrates a real numeric input: =IMAGINARY(4) returns zero.

The imaginary coefficient carries its sign. A value written as 5−i has coefficient −1, not positive one. The imaginary term is that coefficient multiplied by the imaginary unit; the returned coefficient itself is a real number suitable for a numeric helper column.

The dedicated page does not give a complete parsing or error matrix. Its numeric example establishes that particular real-number control, not every Boolean, blank, numeric-text or malformed-string conversion.

Enter only the first column as text in A2:A5. Use =IMAGINARY(A2) in B2 and fill down.

=SUM(B2:B5) returns six. The last two negative coefficients reduce that total; taking absolute values first would answer a different question.

For a j-notation example, Microsoft’s documented =IMAGINARY("0-j") returns −1. The absent written coefficient before j means one, and the preceding minus sign makes it negative.

=IMAGINARY(4) returns zero because a real number has no imaginary component. Zero in the extracted column is therefore a legitimate result, not inherently an error or evidence of a missing input.

For a constructed numeric record, enter 7 in D2 and 0 in E2, then use =IMAGINARY(COMPLEX(D2,E2)). Its independently expected coefficient is zero. COMPLEX keeps the two input coefficients explicit.

A physically empty source cell or a formula returning empty-looking text is a separate case. This guide does not assign those cases the same coercion behavior merely because a genuine real number has imaginary coefficient zero.

For the first fixture, enter =IMREAL(A2) in C2 and fill down. Expected real coefficients are 4, −2, 5 and 0.

In D2 use =COMPLEX(C2,B2) and fill down. The reconstructed quantities are 4+3i, −2+6i, 5−i and −2i. IMREAL supplies the other coordinate; the original text may have included a redundant zero term that the reconstruction need not preserve.

Checking both components is stronger than comparing only B. For example, 4+3i and −2+3i share imaginary coefficient three but are different complex values.

For each original value in A2:A5, use =IMAGINARY(IMCONJUGATE(A2)), filling down. Expected results are −3, −6, 1 and 2.

Conjugation keeps the real coefficient and reverses the imaginary coefficient. Therefore the sum of the original and conjugated imaginary coefficients is zero for every row. This gives a simple signed check without requiring the displayed complex strings to have identical formatting.

IMCONJUGATE changes a sign; it does not take an absolute value of the imaginary coefficient. A negative original coefficient becomes positive under conjugation.

Multiplication by i sends a+bi to −b+ai. For the first record, =IMPRODUCT(A2,"i") has expected result −3+4i, and =IMAGINARY(IMPRODUCT(A2,"i")) returns four.

That result is the original real coefficient, not the original imaginary coefficient three. Applying the same operation a second time gives −4−3i, whose imaginary coefficient is −3.

This is a useful control for sign and coordinate-order mistakes. IMPRODUCT performs the complex multiplication; ordinary multiplication of selected numeric coefficients alone would not represent the same transformation.

For 4+3i multiplied by 1−2i, the imaginary coefficient is 4×(−2)+3×1=−5. The complete product is 10−5i.

=IMAGINARY(IMPRODUCT("4+3i","1-2i")) therefore has expected result −5. Multiplying only the two imaginary coefficients gives −6, which is not the imaginary coefficient of the product.

Keep the full component formula visible when verifying a derived result. Real and imaginary terms interact through complex arithmetic rather than through independent coordinatewise multiplication.

All worked strings use documented lowercase i/j notation or values produced by COMPLEX. The reference does not pin a complete malformed-text error table, general range-coercion behavior or extreme-value precision limits.

A rounded display of a coefficient is not an exact-equality proof. These examples use small exact components and independently calculated outputs; native Excel parsing, display and error precedence were not executed.

• Microsoft IMAGINARY reference.
• Editorial testing standards.

Expected outputs are independently calculated examples or documented rules, not captured native Excel results. Formulas use English function names and comma argument separators. Locale, rendering and boundary restrictions are stated where relevant.