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Simplifying 4x + -1y + (2x + y) * i = 5 + 7i Reorder the terms for easier multiplication: 4x + -1y + i(2x + y) = 5 + 7i 4x + -1y + (2x * i + y * i) = 5 + 7i 4x + -1y + (2ix + iy) = 5 + 7i Reorder the terms: 2ix + iy + 4x + -1y = 5 + 7i Solving 2ix + iy + 4x + -1y = 5 + 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 + 4x + -7i + -1y = 5 + 7i + -7i Reorder the terms: -7i + 2ix + iy + 4x + -1y = 5 + 7i + -7i Combine like terms: 7i + -7i = 0 -7i + 2ix + iy + 4x + -1y = 5 + 0 -7i + 2ix + iy + 4x + -1y = 5 Add '-4x' to each side of the equation. -7i + 2ix + iy + 4x + -4x + -1y = 5 + -4x Combine like terms: 4x + -4x = 0 -7i + 2ix + iy + 0 + -1y = 5 + -4x -7i + 2ix + iy + -1y = 5 + -4x Add 'y' to each side of the equation. -7i + 2ix + iy + -1y + y = 5 + -4x + y Combine like terms: -1y + y = 0 -7i + 2ix + iy + 0 = 5 + -4x + y -7i + 2ix + iy = 5 + -4x + y Reorder the terms: -5 + -7i + 2ix + iy + 4x + -1y = 5 + -4x + y + -5 + 4x + -1y Reorder the terms: -5 + -7i + 2ix + iy + 4x + -1y = 5 + -5 + -4x + 4x + y + -1y Combine like terms: 5 + -5 = 0 -5 + -7i + 2ix + iy + 4x + -1y = 0 + -4x + 4x + y + -1y -5 + -7i + 2ix + iy + 4x + -1y = -4x + 4x + y + -1y Combine like terms: -4x + 4x = 0 -5 + -7i + 2ix + iy + 4x + -1y = 0 + y + -1y -5 + -7i + 2ix + iy + 4x + -1y = y + -1y Combine like terms: y + -1y = 0 -5 + -7i + 2ix + iy + 4x + -1y = 0 The solution to this equation could not be determined.
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