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Simplifying (2 + -1i) * x + (1 + 2i) * y = 10i Reorder the terms for easier multiplication: x(2 + -1i) + (1 + 2i) * y = 10i (2 * x + -1i * x) + (1 + 2i) * y = 10i Reorder the terms: (-1ix + 2x) + (1 + 2i) * y = 10i (-1ix + 2x) + (1 + 2i) * y = 10i Reorder the terms for easier multiplication: -1ix + 2x + y(1 + 2i) = 10i -1ix + 2x + (1 * y + 2i * y) = 10i Reorder the terms: -1ix + 2x + (2iy + 1y) = 10i -1ix + 2x + (2iy + 1y) = 10i Reorder the terms: -1ix + 2iy + 2x + 1y = 10i Solving -1ix + 2iy + 2x + 1y = 10i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-10i' to each side of the equation. -1ix + 2iy + 2x + -10i + 1y = 10i + -10i Reorder the terms: -10i + -1ix + 2iy + 2x + 1y = 10i + -10i Combine like terms: 10i + -10i = 0 -10i + -1ix + 2iy + 2x + 1y = 0 Add '-2x' to each side of the equation. -10i + -1ix + 2iy + 2x + -2x + 1y = 0 + -2x Combine like terms: 2x + -2x = 0 -10i + -1ix + 2iy + 0 + 1y = 0 + -2x -10i + -1ix + 2iy + 1y = 0 + -2x Remove the zero: -10i + -1ix + 2iy + 1y = -2x Add '-1y' to each side of the equation. -10i + -1ix + 2iy + 1y + -1y = -2x + -1y Combine like terms: 1y + -1y = 0 -10i + -1ix + 2iy + 0 = -2x + -1y -10i + -1ix + 2iy = -2x + -1y Reorder the terms: -10i + -1ix + 2iy + 2x + y = -2x + 2x + -1y + y Combine like terms: -2x + 2x = 0 -10i + -1ix + 2iy + 2x + y = 0 + -1y + y -10i + -1ix + 2iy + 2x + y = -1y + y Combine like terms: -1y + y = 0 -10i + -1ix + 2iy + 2x + y = 0 The solution to this equation could not be determined.
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