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Simplifying x(3 + 4i) + 2y(2 + 3i) = 2i (3 * x + 4i * x) + 2y(2 + 3i) = 2i Reorder the terms: (4ix + 3x) + 2y(2 + 3i) = 2i (4ix + 3x) + 2y(2 + 3i) = 2i 4ix + 3x + (2 * 2y + 3i * 2y) = 2i Reorder the terms: 4ix + 3x + (6iy + 4y) = 2i 4ix + 3x + (6iy + 4y) = 2i Reorder the terms: 4ix + 6iy + 3x + 4y = 2i Solving 4ix + 6iy + 3x + 4y = 2i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2i' to each side of the equation. 4ix + 6iy + 3x + -2i + 4y = 2i + -2i Reorder the terms: -2i + 4ix + 6iy + 3x + 4y = 2i + -2i Combine like terms: 2i + -2i = 0 -2i + 4ix + 6iy + 3x + 4y = 0 Add '-3x' to each side of the equation. -2i + 4ix + 6iy + 3x + -3x + 4y = 0 + -3x Combine like terms: 3x + -3x = 0 -2i + 4ix + 6iy + 0 + 4y = 0 + -3x -2i + 4ix + 6iy + 4y = 0 + -3x Remove the zero: -2i + 4ix + 6iy + 4y = -3x Add '-4y' to each side of the equation. -2i + 4ix + 6iy + 4y + -4y = -3x + -4y Combine like terms: 4y + -4y = 0 -2i + 4ix + 6iy + 0 = -3x + -4y -2i + 4ix + 6iy = -3x + -4y Reorder the terms: -2i + 4ix + 6iy + 3x + 4y = -3x + 3x + -4y + 4y Combine like terms: -3x + 3x = 0 -2i + 4ix + 6iy + 3x + 4y = 0 + -4y + 4y -2i + 4ix + 6iy + 3x + 4y = -4y + 4y Combine like terms: -4y + 4y = 0 -2i + 4ix + 6iy + 3x + 4y = 0 The solution to this equation could not be determined.
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