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Simplifying (1 + i) * x3 + (1 + 2i) * x2 + -1(1 + i) * x + -1(1 + 2i) = 0 Reorder the terms for easier multiplication: x3(1 + i) + (1 + 2i) * x2 + -1(1 + i) * x + -1(1 + 2i) = 0 (1 * x3 + i * x3) + (1 + 2i) * x2 + -1(1 + i) * x + -1(1 + 2i) = 0 Reorder the terms: (ix3 + 1x3) + (1 + 2i) * x2 + -1(1 + i) * x + -1(1 + 2i) = 0 (ix3 + 1x3) + (1 + 2i) * x2 + -1(1 + i) * x + -1(1 + 2i) = 0 Reorder the terms for easier multiplication: ix3 + 1x3 + x2(1 + 2i) + -1(1 + i) * x + -1(1 + 2i) = 0 ix3 + 1x3 + (1 * x2 + 2i * x2) + -1(1 + i) * x + -1(1 + 2i) = 0 Reorder the terms: ix3 + 1x3 + (2ix2 + 1x2) + -1(1 + i) * x + -1(1 + 2i) = 0 ix3 + 1x3 + (2ix2 + 1x2) + -1(1 + i) * x + -1(1 + 2i) = 0 Reorder the terms for easier multiplication: ix3 + 1x3 + 2ix2 + 1x2 + -1x(1 + i) + -1(1 + 2i) = 0 ix3 + 1x3 + 2ix2 + 1x2 + (1 * -1x + i * -1x) + -1(1 + 2i) = 0 Reorder the terms: ix3 + 1x3 + 2ix2 + 1x2 + (-1ix + -1x) + -1(1 + 2i) = 0 ix3 + 1x3 + 2ix2 + 1x2 + (-1ix + -1x) + -1(1 + 2i) = 0 ix3 + 1x3 + 2ix2 + 1x2 + -1ix + -1x + (1 * -1 + 2i * -1) = 0 ix3 + 1x3 + 2ix2 + 1x2 + -1ix + -1x + (-1 + -2i) = 0 Reorder the terms: -1 + -2i + -1ix + 2ix2 + ix3 + -1x + 1x2 + 1x3 = 0 Solving -1 + -2i + -1ix + 2ix2 + ix3 + -1x + 1x2 + 1x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -2i + -1ix + 2ix2 + ix3 + -1x + 1x2 + 1 + 1x3 = 0 + 1 Reorder the terms: -1 + 1 + -2i + -1ix + 2ix2 + ix3 + -1x + 1x2 + 1x3 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2i + -1ix + 2ix2 + ix3 + -1x + 1x2 + 1x3 = 0 + 1 -2i + -1ix + 2ix2 + ix3 + -1x + 1x2 + 1x3 = 0 + 1 Combine like terms: 0 + 1 = 1 -2i + -1ix + 2ix2 + ix3 + -1x + 1x2 + 1x3 = 1 Add 'x' to each side of the equation. -2i + -1ix + 2ix2 + ix3 + -1x + 1x2 + x + 1x3 = 1 + x Reorder the terms: -2i + -1ix + 2ix2 + ix3 + -1x + x + 1x2 + 1x3 = 1 + x Combine like terms: -1x + x = 0 -2i + -1ix + 2ix2 + ix3 + 0 + 1x2 + 1x3 = 1 + x -2i + -1ix + 2ix2 + ix3 + 1x2 + 1x3 = 1 + x Add '-1x2' to each side of the equation. -2i + -1ix + 2ix2 + ix3 + 1x2 + -1x2 + 1x3 = 1 + x + -1x2 Combine like terms: 1x2 + -1x2 = 0 -2i + -1ix + 2ix2 + ix3 + 0 + 1x3 = 1 + x + -1x2 -2i + -1ix + 2ix2 + ix3 + 1x3 = 1 + x + -1x2 Add '-1x3' to each side of the equation. -2i + -1ix + 2ix2 + ix3 + 1x3 + -1x3 = 1 + x + -1x2 + -1x3 Combine like terms: 1x3 + -1x3 = 0 -2i + -1ix + 2ix2 + ix3 + 0 = 1 + x + -1x2 + -1x3 -2i + -1ix + 2ix2 + ix3 = 1 + x + -1x2 + -1x3 Reorder the terms: -1 + -2i + -1ix + 2ix2 + ix3 + -1x + x2 + x3 = 1 + x + -1x2 + -1x3 + -1 + -1x + x2 + x3 Reorder the terms: -1 + -2i + -1ix + 2ix2 + ix3 + -1x + x2 + x3 = 1 + -1 + x + -1x + -1x2 + x2 + -1x3 + x3 Combine like terms: 1 + -1 = 0 -1 + -2i + -1ix + 2ix2 + ix3 + -1x + x2 + x3 = 0 + x + -1x + -1x2 + x2 + -1x3 + x3 -1 + -2i + -1ix + 2ix2 + ix3 + -1x + x2 + x3 = x + -1x + -1x2 + x2 + -1x3 + x3 Combine like terms: x + -1x = 0 -1 + -2i + -1ix + 2ix2 + ix3 + -1x + x2 + x3 = 0 + -1x2 + x2 + -1x3 + x3 -1 + -2i + -1ix + 2ix2 + ix3 + -1x + x2 + x3 = -1x2 + x2 + -1x3 + x3 Combine like terms: -1x2 + x2 = 0 -1 + -2i + -1ix + 2ix2 + ix3 + -1x + x2 + x3 = 0 + -1x3 + x3 -1 + -2i + -1ix + 2ix2 + ix3 + -1x + x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -1 + -2i + -1ix + 2ix2 + ix3 + -1x + x2 + x3 = 0 The solution to this equation could not be determined.
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