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Simplifying (x + 2y) + (4x + -3y) * i = (2x + -1) + (y + -6) * i Remove parenthesis around (x + 2y) x + 2y + (4x + -3y) * i = (2x + -1) + (y + -6) * i Reorder the terms for easier multiplication: x + 2y + i(4x + -3y) = (2x + -1) + (y + -6) * i x + 2y + (4x * i + -3y * i) = (2x + -1) + (y + -6) * i x + 2y + (4ix + -3iy) = (2x + -1) + (y + -6) * i Reorder the terms: 4ix + -3iy + x + 2y = (2x + -1) + (y + -6) * i Reorder the terms: 4ix + -3iy + x + 2y = (-1 + 2x) + (y + -6) * i Remove parenthesis around (-1 + 2x) 4ix + -3iy + x + 2y = -1 + 2x + (y + -6) * i Reorder the terms: 4ix + -3iy + x + 2y = -1 + 2x + (-6 + y) * i Reorder the terms for easier multiplication: 4ix + -3iy + x + 2y = -1 + 2x + i(-6 + y) 4ix + -3iy + x + 2y = -1 + 2x + (-6 * i + y * i) 4ix + -3iy + x + 2y = -1 + 2x + (-6i + iy) Reorder the terms: 4ix + -3iy + x + 2y = -1 + -6i + iy + 2x Solving 4ix + -3iy + x + 2y = -1 + -6i + iy + 2x 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. 4ix + -3iy + x + 6i + 2y = -1 + -6i + iy + 6i + 2x Reorder the terms: 6i + 4ix + -3iy + x + 2y = -1 + -6i + iy + 6i + 2x Reorder the terms: 6i + 4ix + -3iy + x + 2y = -1 + -6i + 6i + iy + 2x Combine like terms: -6i + 6i = 0 6i + 4ix + -3iy + x + 2y = -1 + 0 + iy + 2x 6i + 4ix + -3iy + x + 2y = -1 + iy + 2x Add '-1iy' to each side of the equation. 6i + 4ix + -3iy + x + -1iy + 2y = -1 + iy + -1iy + 2x Reorder the terms: 6i + 4ix + -3iy + -1iy + x + 2y = -1 + iy + -1iy + 2x Combine like terms: -3iy + -1iy = -4iy 6i + 4ix + -4iy + x + 2y = -1 + iy + -1iy + 2x Combine like terms: iy + -1iy = 0 6i + 4ix + -4iy + x + 2y = -1 + 0 + 2x 6i + 4ix + -4iy + x + 2y = -1 + 2x Add '-1x' to each side of the equation. 6i + 4ix + -4iy + x + -1x + 2y = -1 + 2x + -1x Combine like terms: x + -1x = 0 6i + 4ix + -4iy + 0 + 2y = -1 + 2x + -1x 6i + 4ix + -4iy + 2y = -1 + 2x + -1x Combine like terms: 2x + -1x = 1x 6i + 4ix + -4iy + 2y = -1 + 1x Add '-2y' to each side of the equation. 6i + 4ix + -4iy + 2y + -2y = -1 + 1x + -2y Combine like terms: 2y + -2y = 0 6i + 4ix + -4iy + 0 = -1 + 1x + -2y 6i + 4ix + -4iy = -1 + 1x + -2y Reorder the terms: 1 + 6i + 4ix + -4iy + -1x + 2y = -1 + 1x + -2y + 1 + -1x + 2y Reorder the terms: 1 + 6i + 4ix + -4iy + -1x + 2y = -1 + 1 + 1x + -1x + -2y + 2y Combine like terms: -1 + 1 = 0 1 + 6i + 4ix + -4iy + -1x + 2y = 0 + 1x + -1x + -2y + 2y 1 + 6i + 4ix + -4iy + -1x + 2y = 1x + -1x + -2y + 2y Combine like terms: 1x + -1x = 0 1 + 6i + 4ix + -4iy + -1x + 2y = 0 + -2y + 2y 1 + 6i + 4ix + -4iy + -1x + 2y = -2y + 2y Combine like terms: -2y + 2y = 0 1 + 6i + 4ix + -4iy + -1x + 2y = 0 The solution to this equation could not be determined.
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