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Simplifying (5 + i) * x + 1 + -3i = (2 + -3i) * x + 2 + -1i Reorder the terms for easier multiplication: x(5 + i) + 1 + -3i = (2 + -3i) * x + 2 + -1i (5 * x + i * x) + 1 + -3i = (2 + -3i) * x + 2 + -1i Reorder the terms: (ix + 5x) + 1 + -3i = (2 + -3i) * x + 2 + -1i (ix + 5x) + 1 + -3i = (2 + -3i) * x + 2 + -1i Reorder the terms: 1 + -3i + ix + 5x = (2 + -3i) * x + 2 + -1i Reorder the terms for easier multiplication: 1 + -3i + ix + 5x = x(2 + -3i) + 2 + -1i 1 + -3i + ix + 5x = (2 * x + -3i * x) + 2 + -1i Reorder the terms: 1 + -3i + ix + 5x = (-3ix + 2x) + 2 + -1i 1 + -3i + ix + 5x = (-3ix + 2x) + 2 + -1i Reorder the terms: 1 + -3i + ix + 5x = 2 + -1i + -3ix + 2x Solving 1 + -3i + ix + 5x = 2 + -1i + -3ix + 2x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i' to each side of the equation. 1 + -3i + ix + i + 5x = 2 + -1i + -3ix + i + 2x Reorder the terms: 1 + -3i + i + ix + 5x = 2 + -1i + -3ix + i + 2x Combine like terms: -3i + i = -2i 1 + -2i + ix + 5x = 2 + -1i + -3ix + i + 2x Reorder the terms: 1 + -2i + ix + 5x = 2 + -1i + i + -3ix + 2x Combine like terms: -1i + i = 0 1 + -2i + ix + 5x = 2 + 0 + -3ix + 2x 1 + -2i + ix + 5x = 2 + -3ix + 2x Add '3ix' to each side of the equation. 1 + -2i + ix + 3ix + 5x = 2 + -3ix + 3ix + 2x Combine like terms: ix + 3ix = 4ix 1 + -2i + 4ix + 5x = 2 + -3ix + 3ix + 2x Combine like terms: -3ix + 3ix = 0 1 + -2i + 4ix + 5x = 2 + 0 + 2x 1 + -2i + 4ix + 5x = 2 + 2x Add '-1' to each side of the equation. 1 + -2i + 4ix + -1 + 5x = 2 + -1 + 2x Reorder the terms: 1 + -1 + -2i + 4ix + 5x = 2 + -1 + 2x Combine like terms: 1 + -1 = 0 0 + -2i + 4ix + 5x = 2 + -1 + 2x -2i + 4ix + 5x = 2 + -1 + 2x Combine like terms: 2 + -1 = 1 -2i + 4ix + 5x = 1 + 2x Add '-5x' to each side of the equation. -2i + 4ix + 5x + -5x = 1 + 2x + -5x Combine like terms: 5x + -5x = 0 -2i + 4ix + 0 = 1 + 2x + -5x -2i + 4ix = 1 + 2x + -5x Combine like terms: 2x + -5x = -3x -2i + 4ix = 1 + -3x Reorder the terms: -1 + -2i + 4ix + 3x = 1 + -3x + -1 + 3x Reorder the terms: -1 + -2i + 4ix + 3x = 1 + -1 + -3x + 3x Combine like terms: 1 + -1 = 0 -1 + -2i + 4ix + 3x = 0 + -3x + 3x -1 + -2i + 4ix + 3x = -3x + 3x Combine like terms: -3x + 3x = 0 -1 + -2i + 4ix + 3x = 0 The solution to this equation could not be determined.
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