Complex Linear System Solver

Solve a complex-coefficient system of linear equations Ax=b by entering the augmented matrix. Uses complex-number Gaussian elimination and reports the complex solution vector, number of variables, and uniqueness.

Input

Enter the augmented matrix of the complex linear system Ax=b. Each line is one equation.

Each entry is in a+bi form (e.g. 3, -2, i, 3+4i, 0.5-1.5i). The last entry of each row is the right-hand side b.

Augmented matrix [A | b]

Result

Complex solution

x1 = 1 − 1i

x2 = 1 − 1i

Variables

Unique solution

Yes

Solution vector

x1	1 − 1i
x2	1 − 1i

How it works

Enter each entry in a+bi form, e.g. 3, -2, i, -i, 2i, 3+4i, 0.5-1.5i. The imaginary unit is i (j is also accepted).
Each line is one row of the augmented matrix: the last entry is the right-hand side b and the rest are the coefficients A. Separate entries with spaces or commas.
You need n equations for n variables (a square system). If the coefficient matrix A is non-singular, the solution is unique.
The solver uses complex Gaussian-Jordan elimination with partial pivoting (largest absolute pivot) for numerical stability.
If a pivot magnitude is essentially zero (the coefficient matrix is singular), the system has no unique solution and an error is shown.
For display, real or imaginary parts below about 1e-9 in magnitude are treated as 0 and rounded.

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