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Simplifying 2x + 3yi + 4xi + -2y + -5 + 10i = x + y + 2 + -1(y + -1x + -5) * i Reorder the terms: -5 + 10i + 4ix + 3iy + 2x + -2y = x + y + 2 + -1(y + -1x + -5) * i Reorder the terms: -5 + 10i + 4ix + 3iy + 2x + -2y = x + y + 2 + -1(-5 + -1x + y) * i Reorder the terms for easier multiplication: -5 + 10i + 4ix + 3iy + 2x + -2y = x + y + 2 + -1i(-5 + -1x + y) -5 + 10i + 4ix + 3iy + 2x + -2y = x + y + 2 + (-5 * -1i + -1x * -1i + y * -1i) -5 + 10i + 4ix + 3iy + 2x + -2y = x + y + 2 + (5i + 1ix + -1iy) Reorder the terms: -5 + 10i + 4ix + 3iy + 2x + -2y = 2 + 5i + 1ix + -1iy + x + y Solving -5 + 10i + 4ix + 3iy + 2x + -2y = 2 + 5i + 1ix + -1iy + x + y 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. -5 + 10i + 4ix + 3iy + 2x + -5i + -2y = 2 + 5i + 1ix + -1iy + x + -5i + y Reorder the terms: -5 + 10i + -5i + 4ix + 3iy + 2x + -2y = 2 + 5i + 1ix + -1iy + x + -5i + y Combine like terms: 10i + -5i = 5i -5 + 5i + 4ix + 3iy + 2x + -2y = 2 + 5i + 1ix + -1iy + x + -5i + y Reorder the terms: -5 + 5i + 4ix + 3iy + 2x + -2y = 2 + 5i + -5i + 1ix + -1iy + x + y Combine like terms: 5i + -5i = 0 -5 + 5i + 4ix + 3iy + 2x + -2y = 2 + 0 + 1ix + -1iy + x + y -5 + 5i + 4ix + 3iy + 2x + -2y = 2 + 1ix + -1iy + x + y Add '-1ix' to each side of the equation. -5 + 5i + 4ix + 3iy + 2x + -1ix + -2y = 2 + 1ix + -1iy + x + -1ix + y Reorder the terms: -5 + 5i + 4ix + -1ix + 3iy + 2x + -2y = 2 + 1ix + -1iy + x + -1ix + y Combine like terms: 4ix + -1ix = 3ix -5 + 5i + 3ix + 3iy + 2x + -2y = 2 + 1ix + -1iy + x + -1ix + y Reorder the terms: -5 + 5i + 3ix + 3iy + 2x + -2y = 2 + 1ix + -1ix + -1iy + x + y Combine like terms: 1ix + -1ix = 0 -5 + 5i + 3ix + 3iy + 2x + -2y = 2 + 0 + -1iy + x + y -5 + 5i + 3ix + 3iy + 2x + -2y = 2 + -1iy + x + y Add 'iy' to each side of the equation. -5 + 5i + 3ix + 3iy + 2x + iy + -2y = 2 + -1iy + x + iy + y Reorder the terms: -5 + 5i + 3ix + 3iy + iy + 2x + -2y = 2 + -1iy + x + iy + y Combine like terms: 3iy + iy = 4iy -5 + 5i + 3ix + 4iy + 2x + -2y = 2 + -1iy + x + iy + y Reorder the terms: -5 + 5i + 3ix + 4iy + 2x + -2y = 2 + -1iy + iy + x + y Combine like terms: -1iy + iy = 0 -5 + 5i + 3ix + 4iy + 2x + -2y = 2 + 0 + x + y -5 + 5i + 3ix + 4iy + 2x + -2y = 2 + x + y Add '5' to each side of the equation. -5 + 5i + 3ix + 4iy + 2x + 5 + -2y = 2 + x + 5 + y Reorder the terms: -5 + 5 + 5i + 3ix + 4iy + 2x + -2y = 2 + x + 5 + y Combine like terms: -5 + 5 = 0 0 + 5i + 3ix + 4iy + 2x + -2y = 2 + x + 5 + y 5i + 3ix + 4iy + 2x + -2y = 2 + x + 5 + y Reorder the terms: 5i + 3ix + 4iy + 2x + -2y = 2 + 5 + x + y Combine like terms: 2 + 5 = 7 5i + 3ix + 4iy + 2x + -2y = 7 + x + y Add '-2x' to each side of the equation. 5i + 3ix + 4iy + 2x + -2x + -2y = 7 + x + -2x + y Combine like terms: 2x + -2x = 0 5i + 3ix + 4iy + 0 + -2y = 7 + x + -2x + y 5i + 3ix + 4iy + -2y = 7 + x + -2x + y Combine like terms: x + -2x = -1x 5i + 3ix + 4iy + -2y = 7 + -1x + y Add '2y' to each side of the equation. 5i + 3ix + 4iy + -2y + 2y = 7 + -1x + y + 2y Combine like terms: -2y + 2y = 0 5i + 3ix + 4iy + 0 = 7 + -1x + y + 2y 5i + 3ix + 4iy = 7 + -1x + y + 2y Combine like terms: y + 2y = 3y 5i + 3ix + 4iy = 7 + -1x + 3y Reorder the terms: -7 + 5i + 3ix + 4iy + x + -3y = 7 + -1x + 3y + -7 + x + -3y Reorder the terms: -7 + 5i + 3ix + 4iy + x + -3y = 7 + -7 + -1x + x + 3y + -3y Combine like terms: 7 + -7 = 0 -7 + 5i + 3ix + 4iy + x + -3y = 0 + -1x + x + 3y + -3y -7 + 5i + 3ix + 4iy + x + -3y = -1x + x + 3y + -3y Combine like terms: -1x + x = 0 -7 + 5i + 3ix + 4iy + x + -3y = 0 + 3y + -3y -7 + 5i + 3ix + 4iy + x + -3y = 3y + -3y Combine like terms: 3y + -3y = 0 -7 + 5i + 3ix + 4iy + x + -3y = 0 The solution to this equation could not be determined.
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