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