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