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