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Simplifying (3 + 2i) * x + (1 + i) * y = 2 + 6i Reorder the terms for easier multiplication: x(3 + 2i) + (1 + i) * y = 2 + 6i (3 * x + 2i * x) + (1 + i) * y = 2 + 6i Reorder the terms: (2ix + 3x) + (1 + i) * y = 2 + 6i (2ix + 3x) + (1 + i) * y = 2 + 6i Reorder the terms for easier multiplication: 2ix + 3x + y(1 + i) = 2 + 6i 2ix + 3x + (1 * y + i * y) = 2 + 6i Reorder the terms: 2ix + 3x + (iy + 1y) = 2 + 6i 2ix + 3x + (iy + 1y) = 2 + 6i Reorder the terms: 2ix + iy + 3x + 1y = 2 + 6i Solving 2ix + iy + 3x + 1y = 2 + 6i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-6i' to each side of the equation. 2ix + iy + 3x + -6i + 1y = 2 + 6i + -6i Reorder the terms: -6i + 2ix + iy + 3x + 1y = 2 + 6i + -6i Combine like terms: 6i + -6i = 0 -6i + 2ix + iy + 3x + 1y = 2 + 0 -6i + 2ix + iy + 3x + 1y = 2 Add '-3x' to each side of the equation. -6i + 2ix + iy + 3x + -3x + 1y = 2 + -3x Combine like terms: 3x + -3x = 0 -6i + 2ix + iy + 0 + 1y = 2 + -3x -6i + 2ix + iy + 1y = 2 + -3x Add '-1y' to each side of the equation. -6i + 2ix + iy + 1y + -1y = 2 + -3x + -1y Combine like terms: 1y + -1y = 0 -6i + 2ix + iy + 0 = 2 + -3x + -1y -6i + 2ix + iy = 2 + -3x + -1y Reorder the terms: -2 + -6i + 2ix + iy + 3x + y = 2 + -3x + -1y + -2 + 3x + y Reorder the terms: -2 + -6i + 2ix + iy + 3x + y = 2 + -2 + -3x + 3x + -1y + y Combine like terms: 2 + -2 = 0 -2 + -6i + 2ix + iy + 3x + y = 0 + -3x + 3x + -1y + y -2 + -6i + 2ix + iy + 3x + y = -3x + 3x + -1y + y Combine like terms: -3x + 3x = 0 -2 + -6i + 2ix + iy + 3x + y = 0 + -1y + y -2 + -6i + 2ix + iy + 3x + y = -1y + y Combine like terms: -1y + y = 0 -2 + -6i + 2ix + iy + 3x + y = 0 The solution to this equation could not be determined.
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