IMDIV in Excel: Divide Complex Values and Verify the Denominator

• 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 IMDIV reference. Documentation and independent models; no native Excel execution or wider platform certification.

=IMDIV(inumber1,inumber2)

Microsoft identifies inumber1 as the numerator and inumber2 as the denominator. Its equation image gives, for (a+bi)/(c+di), real coefficient (ac+bd)/(c²+d²) and imaginary coefficient (bc−ad)/(c²+d²).

The denominator is the squared magnitude of the divisor. It is positive for every nonzero complex divisor and zero only when both of its coefficients are zero.

The dedicated page does not state the native error code for zero division or provide a complete invalid-input matrix. The guide holds those display details rather than importing the ordinary numeric division error. COMPLEX can construct valid inputs from numeric coefficients.

Enter only the first two text columns in A1:B4. Put =IMDIV(A2,B2) in C2 and fill through C4. The last column gives independently expected quantities.

The middle row has components −2/5 and 11/5. Its displayed decimal form is a readable expectation, not a promise of an exact full-precision text rendering in every Excel build.

Check the operands before dividing. Reversing numerator and denominator generally changes both components rather than simply changing their signs.

For (4+3i)/(1−2i), the shared denominator is 1²+(−2)²=5. The real numerator is 4×1+3×(−2)=−2. The imaginary numerator is 3×1−4×(−2)=11.

Numeric helper formulas are:

=(4*1+3*(-2))/(1^2+(-2)^2)
=(3*1-4*(-2))/(1^2+(-2)^2)

Expected components are −0.4 and 2.2. Compare these with IMREAL and IMAGINARY applied to the IMDIV result.

The sign in bc−ad matters. Swapping that subtraction would reverse the quotient’s imaginary coefficient and produce a different quantity.

The denominator 1−2i has conjugate 1+2i. Multiplying the original numerator by that conjugate gives −2+11i. Multiplying the denominator by its conjugate gives five with zero imaginary component.

The quotient is therefore (−2+11i)/5, matching the previous calculation. IMCONJUGATE and IMPRODUCT expose each algebraic step.

This derivation explains the squared-magnitude denominator. It is not a recommendation to replace the native function with a manually squared algorithm for extremely large or tiny coefficients; their numerical stability may differ.

For the first fixture, use =IMPRODUCT(C2,B2) and fill through row 4. The expected recovered quantities are 8−i, 4+3i and 10+11i.

For the middle row, (−0.4+2.2i)(1−2i) has real coefficient −0.4+4.4=4 and imaginary coefficient 0.8+2.2=3. Fractions −2/5 and 11/5 make this check exact in the independent mathematical model.

In a native floating-point workbook, inspect component differences using an appropriate stated tolerance rather than requiring full displayed strings to match character for character.

The quotient (4+3i)/(1−2i) has components −0.4 and 2.2. Reversing the operands gives (1−2i)/(4+3i), whose components are −0.08 and −0.44.

The reversed quotient is the reciprocal of the original, not its negative. Their product has real coefficient one and imaginary coefficient zero mathematically.

For the reciprocal of 4+3i itself, divide 1+0i by 4+3i. The components are 4/25 and −3/25, or 0.16 and −0.12. The conjugate alone, 4−3i, is missing the division by 25.

Multiplying both numerator and denominator by the same nonzero real factor leaves the quotient unchanged. Scaling the middle pair by two gives (8+6i)/(2−4i), still −0.4+2.2i.

A divisor with components zero and zero has squared magnitude zero. It does not define a quotient, and returning a fabricated zero would conceal the problem. Validate that prerequisite separately; native zero-error punctuation and code remain unverified by the cited page.

All examples use explicit valid complex inputs with consistent i notation. Mixed suffix handling, malformed strings, general blank coercion and extreme numeric behavior remain outside this review. Expected outputs are independently calculated, with no native Excel execution.

• Microsoft IMDIV 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.