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Simplifying (6x + yi) + -1(y + 2xi) = 1 + 7i Reorder the terms: (iy + 6x) + -1(y + 2xi) = 1 + 7i Remove parenthesis around (iy + 6x) iy + 6x + -1(y + 2xi) = 1 + 7i Reorder the terms: iy + 6x + -1(2ix + y) = 1 + 7i iy + 6x + (2ix * -1 + y * -1) = 1 + 7i iy + 6x + (-2ix + -1y) = 1 + 7i Reorder the terms: -2ix + iy + 6x + -1y = 1 + 7i Solving -2ix + iy + 6x + -1y = 1 + 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. -2ix + iy + 6x + -7i + -1y = 1 + 7i + -7i Reorder the terms: -7i + -2ix + iy + 6x + -1y = 1 + 7i + -7i Combine like terms: 7i + -7i = 0 -7i + -2ix + iy + 6x + -1y = 1 + 0 -7i + -2ix + iy + 6x + -1y = 1 Add '-6x' to each side of the equation. -7i + -2ix + iy + 6x + -6x + -1y = 1 + -6x Combine like terms: 6x + -6x = 0 -7i + -2ix + iy + 0 + -1y = 1 + -6x -7i + -2ix + iy + -1y = 1 + -6x Add 'y' to each side of the equation. -7i + -2ix + iy + -1y + y = 1 + -6x + y Combine like terms: -1y + y = 0 -7i + -2ix + iy + 0 = 1 + -6x + y -7i + -2ix + iy = 1 + -6x + y Reorder the terms: -1 + -7i + -2ix + iy + 6x + -1y = 1 + -6x + y + -1 + 6x + -1y Reorder the terms: -1 + -7i + -2ix + iy + 6x + -1y = 1 + -1 + -6x + 6x + y + -1y Combine like terms: 1 + -1 = 0 -1 + -7i + -2ix + iy + 6x + -1y = 0 + -6x + 6x + y + -1y -1 + -7i + -2ix + iy + 6x + -1y = -6x + 6x + y + -1y Combine like terms: -6x + 6x = 0 -1 + -7i + -2ix + iy + 6x + -1y = 0 + y + -1y -1 + -7i + -2ix + iy + 6x + -1y = y + -1y Combine like terms: y + -1y = 0 -1 + -7i + -2ix + iy + 6x + -1y = 0 The solution to this equation could not be determined.
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