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Consider the 2×2 linear system (A+iB)(x +iy) = c+id with complex entries in component form:
(a11 + ib11)(x1 + iy1) + (a12 + ib12)(x2 + iy2) = c1 + id1,
(a11 + ib21)(x1 + iy1) + (a22 + ib22)(x2 + iy2) = c2 + id2.
a. Use the properties of complex numbers to convert this system to the equivalent 4×4 real linear
system
Ax − By = c,
Bx + Ay = d.
b. Solve the linear system
(1 − 2i)(x1 + iy1) + (3 + 2i)(x2 + iy2) = 5 + 2i,
(2 + i)(x1 + iy1) + (4 + 3i)(x2 + iy2) = 4 − i. |
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