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