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Simplifying (x + -2iy) + (y + -3ix) = 2 + 3i Reorder the terms: (-2iy + x) + (y + -3ix) = 2 + 3i Remove parenthesis around (-2iy + x) -2iy + x + (y + -3ix) = 2 + 3i Reorder the terms: -2iy + x + (-3ix + y) = 2 + 3i Remove parenthesis around (-3ix + y) -2iy + x + -3ix + y = 2 + 3i Reorder the terms: -3ix + -2iy + x + y = 2 + 3i Solving -3ix + -2iy + x + y = 2 + 3i 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. -3ix + -2iy + x + -3i + y = 2 + 3i + -3i Reorder the terms: -3i + -3ix + -2iy + x + y = 2 + 3i + -3i Combine like terms: 3i + -3i = 0 -3i + -3ix + -2iy + x + y = 2 + 0 -3i + -3ix + -2iy + x + y = 2 Add '-1x' to each side of the equation. -3i + -3ix + -2iy + x + -1x + y = 2 + -1x Combine like terms: x + -1x = 0 -3i + -3ix + -2iy + 0 + y = 2 + -1x -3i + -3ix + -2iy + y = 2 + -1x Add '-1y' to each side of the equation. -3i + -3ix + -2iy + y + -1y = 2 + -1x + -1y Combine like terms: y + -1y = 0 -3i + -3ix + -2iy + 0 = 2 + -1x + -1y -3i + -3ix + -2iy = 2 + -1x + -1y Reorder the terms: -2 + -3i + -3ix + -2iy + x + y = 2 + -1x + -1y + -2 + x + y Reorder the terms: -2 + -3i + -3ix + -2iy + x + y = 2 + -2 + -1x + x + -1y + y Combine like terms: 2 + -2 = 0 -2 + -3i + -3ix + -2iy + x + y = 0 + -1x + x + -1y + y -2 + -3i + -3ix + -2iy + x + y = -1x + x + -1y + y Combine like terms: -1x + x = 0 -2 + -3i + -3ix + -2iy + x + y = 0 + -1y + y -2 + -3i + -3ix + -2iy + x + y = -1y + y Combine like terms: -1y + y = 0 -2 + -3i + -3ix + -2iy + x + y = 0 The solution to this equation could not be determined.
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