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Simplifying x + -2y + xi + -1yi = 2 + 5i Reorder the terms: ix + -1iy + x + -2y = 2 + 5i Solving ix + -1iy + x + -2y = 2 + 5i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-5i' to each side of the equation. ix + -1iy + x + -5i + -2y = 2 + 5i + -5i Reorder the terms: -5i + ix + -1iy + x + -2y = 2 + 5i + -5i Combine like terms: 5i + -5i = 0 -5i + ix + -1iy + x + -2y = 2 + 0 -5i + ix + -1iy + x + -2y = 2 Add '-1x' to each side of the equation. -5i + ix + -1iy + x + -1x + -2y = 2 + -1x Combine like terms: x + -1x = 0 -5i + ix + -1iy + 0 + -2y = 2 + -1x -5i + ix + -1iy + -2y = 2 + -1x Add '2y' to each side of the equation. -5i + ix + -1iy + -2y + 2y = 2 + -1x + 2y Combine like terms: -2y + 2y = 0 -5i + ix + -1iy + 0 = 2 + -1x + 2y -5i + ix + -1iy = 2 + -1x + 2y Reorder the terms: -2 + -5i + ix + -1iy + x + -2y = 2 + -1x + 2y + -2 + x + -2y Reorder the terms: -2 + -5i + ix + -1iy + x + -2y = 2 + -2 + -1x + x + 2y + -2y Combine like terms: 2 + -2 = 0 -2 + -5i + ix + -1iy + x + -2y = 0 + -1x + x + 2y + -2y -2 + -5i + ix + -1iy + x + -2y = -1x + x + 2y + -2y Combine like terms: -1x + x = 0 -2 + -5i + ix + -1iy + x + -2y = 0 + 2y + -2y -2 + -5i + ix + -1iy + x + -2y = 2y + -2y Combine like terms: 2y + -2y = 0 -2 + -5i + ix + -1iy + x + -2y = 0 The solution to this equation could not be determined.
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