COMPLEX in Excel: Build i or j Representations from Numeric 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 COMPLEX reference. Documentation and independent models; no native Excel execution or wider platform certification.

=COMPLEX(real_num,i_num,[suffix])

The first two arguments are required numeric coefficients. The optional suffix defaults to “i” and may be “i” or “j”. Microsoft documents #VALUE! for a nonnumeric coefficient or an unsupported suffix.

The source also states that functions accepting two or more complex inputs require matching suffixes. Choose one notation for a workflow rather than mixing i and j labels. The two letters represent the same mathematical imaginary unit in this context, not different coefficients.

The displayed representation can simplify when a component is zero. Microsoft’s examples show COMPLEX(0,1) as i and COMPLEX(1,0) as 1. Those displayed forms are not native type-test evidence for every degenerate result.

Enter only the first two numeric columns of this table in A1:B5. The third column shows expected output: calculate C2 with =COMPLEX(A2,B2) and fill through C5.

The imaginary coefficient is the number multiplying i, not a preformatted string such as “4i”. Keep A and B numeric so the components remain available for independent calculations.

In D2 use =COMPLEX(A2,B2,"j") and fill down. The corresponding representations are 3+4j, 2-3j, −2+5j and j. The signs and coefficients remain the same; only the suffix changes. In a spreadsheet string the minus sign is the ordinary hyphen character.

If a report requires a consistent j notation, explicitly supply “j” throughout rather than relying on the default i.

=COMPLEX(3,4) has expected representation 3+4i. Supplying “4i” as the second argument is not the same input: the function requires a numeric imaginary coefficient and documents an error for nonnumeric values.

Likewise, =COMPLEX(3,4,"I") has a documented #VALUE! result because uppercase I is unsupported. A suffix such as “k” is also outside the two allowed choices.

Use cell references to the numeric coefficients when constructing formulas. Building strings by concatenating a plus sign without considering a negative coefficient could create a label such as 2+-3i; COMPLEX expresses the intended form directly.

Put the first number’s coefficients 3 and 4 in F2:G2, and the second number’s coefficients 2 and −1 in H2:I2. The mathematical numbers are 3+4i and 2−i.

A transparent component-based sum is:

=COMPLEX(F2+H2,G2+I2)

The expected representation is 5+3i. The real components add to 5 and the imaginary components add to 3. This example calculates with the numeric coefficients before constructing the representation; it does not claim that ordinary addition of two displayed complex strings performs complex arithmetic.

For the difference, =COMPLEX(F2-H2,G2-I2) gives 1+5i. Retaining the component columns makes each operation inspectable without needing to parse a formatted string back into pieces.

Using the same four coefficient cells, apply i^2=−1:

=COMPLEX(F2*H2-G2*I2,F2*I2+G2*H2)

The real coefficient is 3×2−4×(−1)=10. The imaginary coefficient is 3×(−1)+4×2=5. The independently expected representation is 10+5i.

The two cross-products belong to the imaginary component. Multiplying only corresponding coefficients would produce a different result and would miss the defining i^2=−1 contribution.

For j notation, supply “j” as the final argument to the same construction. Keep that choice consistent with any later functions that consume the representation.

For coefficients 3 and 4, the conjugate is constructed with =COMPLEX(3,-4), giving 3−4i. Multiplying the original and conjugate in the component model produces real 3^2+4^2=25 and imaginary zero.

The mathematical magnitude is =SQRT(3^2+4^2), or 5. SQRT evaluates this numeric helper expression. The coefficient pair, the complex representation, its conjugate and its magnitude are four different outputs.

These examples establish the component arithmetic, not arbitrary parsing, precision or native output-type behavior. Complex operations have their own dedicated function contracts; do not assume that ordinary worksheet operators on a rendered representation implement them. Locale-sensitive decimal rendering and extreme values remain untested.

• Microsoft COMPLEX 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.