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