Complex Number Matrix Multiplication Calculator

Fast complex matrix multiplication for engineers, students, and researchers. Enter matrices of any compatible dimension with a+bi entries. See clean results, intermediate steps, and helpful dimension checks. Validate inputs, swap matrices, and reuse saved presets. Export CSV now, or print to save as PDF.

Should match A Columns.
Matrix A 2 × 2
Matrix B 2 × 2
Example Data

A simple example demonstrating multiplication. Click Load example to insert these values.

Matrix A (2 × 2)
1+2i3-4i
-2i5
Matrix B (2 × 2)
2-i-1+3i
4i
Formula Used
For two matrices A of size m × n and B of size n × p, the product C = A × B is an m × p matrix where the entry at row i, column j is: 
Cij = Σnk=1 Aik · Bkj
With complex entries, multiplication uses (a + bi)(c + di) = (ac − bd) + (ad + bc)i, and addition is element-wise on real and imaginary parts.
How to Use
  1. Choose sizes so columns of A equal rows of B.
  2. Enter complex numbers like 3+2i, -4i, 5, or i.
  3. Optionally enable details to see every dot-product term.
  4. Click Compute A × B to generate the result matrix.
  5. Use Download Result CSV or Save Result as PDF for exports.
FAQs

Use a+bi, a-bi, bi, -bi, i, -i, or real numbers like 7.

Matrix multiplication requires pairwise products along shared dimensions. Otherwise, dot products are undefined.

Choose 0–10 places using the Decimal places control. Exact arithmetic rounds at display time.

Yes. Use Regenerate grids to change sizes, or keep sizes unchanged to reuse inputs.

Check spacing and format. Remove parentheses and ensure only one i appears in each entry.

Use the CSV download for quick imports into Excel, Sheets, or similar tools.
Dimension Rules & Compatibility (Current Selection)
A size2 × 2
B size2 × 2
CompatibilityCompatible: A columns equal B rows
Result size2 × 2
Accepted Input Patterns & Examples
PatternExamplesNotes
a+bi, a-bi3+2i, -1-4iDecimals allowed: 2.75-0.5i
bi, -bi7i, -0.25ii equals 1i, -i equals -1i
Real only5, -12.3Imaginary part is zero
Spacing / parentheses(3+2i), 3 + 2i Sanitized automatically
Arithmetic Identities Used
OperationIdentity
Addition(a+bi)+(c+di)=(a+c)+(b+d)i
Multiplication(a+bi)(c+di)=(ac-bd)+(ad+bc)i
Conjugate\overline{a+bi}=a-bi
Modulus|a+bi|=\sqrt{a^2+b^2}
Worked 2 × 2 Example (Computed)

Using the example matrices above, the product C = A × B is:

16 - 13i -3 + 4i
18 - 4i 6 + 7i