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Simplifying (x + -1y) + (2x + y) * i = 6 + -2i Remove parenthesis around (x + -1y) x + -1y + (2x + y) * i = 6 + -2i Reorder the terms for easier multiplication: x + -1y + i(2x + y) = 6 + -2i x + -1y + (2x * i + y * i) = 6 + -2i x + -1y + (2ix + iy) = 6 + -2i Reorder the terms: 2ix + iy + x + -1y = 6 + -2i Solving 2ix + iy + x + -1y = 6 + -2i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '2i' to each side of the equation. 2ix + iy + x + 2i + -1y = 6 + -2i + 2i Reorder the terms: 2i + 2ix + iy + x + -1y = 6 + -2i + 2i Combine like terms: -2i + 2i = 0 2i + 2ix + iy + x + -1y = 6 + 0 2i + 2ix + iy + x + -1y = 6 Add '-1x' to each side of the equation. 2i + 2ix + iy + x + -1x + -1y = 6 + -1x Combine like terms: x + -1x = 0 2i + 2ix + iy + 0 + -1y = 6 + -1x 2i + 2ix + iy + -1y = 6 + -1x Add 'y' to each side of the equation. 2i + 2ix + iy + -1y + y = 6 + -1x + y Combine like terms: -1y + y = 0 2i + 2ix + iy + 0 = 6 + -1x + y 2i + 2ix + iy = 6 + -1x + y Reorder the terms: -6 + 2i + 2ix + iy + x + -1y = 6 + -1x + y + -6 + x + -1y Reorder the terms: -6 + 2i + 2ix + iy + x + -1y = 6 + -6 + -1x + x + y + -1y Combine like terms: 6 + -6 = 0 -6 + 2i + 2ix + iy + x + -1y = 0 + -1x + x + y + -1y -6 + 2i + 2ix + iy + x + -1y = -1x + x + y + -1y Combine like terms: -1x + x = 0 -6 + 2i + 2ix + iy + x + -1y = 0 + y + -1y -6 + 2i + 2ix + iy + x + -1y = y + -1y Combine like terms: y + -1y = 0 -6 + 2i + 2ix + iy + x + -1y = 0 The solution to this equation could not be determined.
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