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Simplifying x(2 + 3i) + y(5 + -2i) = -8 + 7i (2 * x + 3i * x) + y(5 + -2i) = -8 + 7i Reorder the terms: (3ix + 2x) + y(5 + -2i) = -8 + 7i (3ix + 2x) + y(5 + -2i) = -8 + 7i 3ix + 2x + (5 * y + -2i * y) = -8 + 7i Reorder the terms: 3ix + 2x + (-2iy + 5y) = -8 + 7i 3ix + 2x + (-2iy + 5y) = -8 + 7i Reorder the terms: 3ix + -2iy + 2x + 5y = -8 + 7i Solving 3ix + -2iy + 2x + 5y = -8 + 7i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-7i' to each side of the equation. 3ix + -2iy + 2x + -7i + 5y = -8 + 7i + -7i Reorder the terms: -7i + 3ix + -2iy + 2x + 5y = -8 + 7i + -7i Combine like terms: 7i + -7i = 0 -7i + 3ix + -2iy + 2x + 5y = -8 + 0 -7i + 3ix + -2iy + 2x + 5y = -8 Add '-2x' to each side of the equation. -7i + 3ix + -2iy + 2x + -2x + 5y = -8 + -2x Combine like terms: 2x + -2x = 0 -7i + 3ix + -2iy + 0 + 5y = -8 + -2x -7i + 3ix + -2iy + 5y = -8 + -2x Add '-5y' to each side of the equation. -7i + 3ix + -2iy + 5y + -5y = -8 + -2x + -5y Combine like terms: 5y + -5y = 0 -7i + 3ix + -2iy + 0 = -8 + -2x + -5y -7i + 3ix + -2iy = -8 + -2x + -5y Reorder the terms: 8 + -7i + 3ix + -2iy + 2x + 5y = -8 + -2x + -5y + 8 + 2x + 5y Reorder the terms: 8 + -7i + 3ix + -2iy + 2x + 5y = -8 + 8 + -2x + 2x + -5y + 5y Combine like terms: -8 + 8 = 0 8 + -7i + 3ix + -2iy + 2x + 5y = 0 + -2x + 2x + -5y + 5y 8 + -7i + 3ix + -2iy + 2x + 5y = -2x + 2x + -5y + 5y Combine like terms: -2x + 2x = 0 8 + -7i + 3ix + -2iy + 2x + 5y = 0 + -5y + 5y 8 + -7i + 3ix + -2iy + 2x + 5y = -5y + 5y Combine like terms: -5y + 5y = 0 8 + -7i + 3ix + -2iy + 2x + 5y = 0 The solution to this equation could not be determined.
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