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Simplifying (3 + -2i)(x + y) = 4 + 5i Multiply (3 + -2i) * (x + y) (3(x + y) + -2i * (x + y)) = 4 + 5i ((x * 3 + y * 3) + -2i * (x + y)) = 4 + 5i ((3x + 3y) + -2i * (x + y)) = 4 + 5i (3x + 3y + (x * -2i + y * -2i)) = 4 + 5i (3x + 3y + (-2ix + -2iy)) = 4 + 5i Reorder the terms: (-2ix + -2iy + 3x + 3y) = 4 + 5i (-2ix + -2iy + 3x + 3y) = 4 + 5i Solving -2ix + -2iy + 3x + 3y = 4 + 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. -2ix + -2iy + 3x + -5i + 3y = 4 + 5i + -5i Reorder the terms: -5i + -2ix + -2iy + 3x + 3y = 4 + 5i + -5i Combine like terms: 5i + -5i = 0 -5i + -2ix + -2iy + 3x + 3y = 4 + 0 -5i + -2ix + -2iy + 3x + 3y = 4 Add '-3x' to each side of the equation. -5i + -2ix + -2iy + 3x + -3x + 3y = 4 + -3x Combine like terms: 3x + -3x = 0 -5i + -2ix + -2iy + 0 + 3y = 4 + -3x -5i + -2ix + -2iy + 3y = 4 + -3x Add '-3y' to each side of the equation. -5i + -2ix + -2iy + 3y + -3y = 4 + -3x + -3y Combine like terms: 3y + -3y = 0 -5i + -2ix + -2iy + 0 = 4 + -3x + -3y -5i + -2ix + -2iy = 4 + -3x + -3y Reorder the terms: -4 + -5i + -2ix + -2iy + 3x + 3y = 4 + -3x + -3y + -4 + 3x + 3y Reorder the terms: -4 + -5i + -2ix + -2iy + 3x + 3y = 4 + -4 + -3x + 3x + -3y + 3y Combine like terms: 4 + -4 = 0 -4 + -5i + -2ix + -2iy + 3x + 3y = 0 + -3x + 3x + -3y + 3y -4 + -5i + -2ix + -2iy + 3x + 3y = -3x + 3x + -3y + 3y Combine like terms: -3x + 3x = 0 -4 + -5i + -2ix + -2iy + 3x + 3y = 0 + -3y + 3y -4 + -5i + -2ix + -2iy + 3x + 3y = -3y + 3y Combine like terms: -3y + 3y = 0 -4 + -5i + -2ix + -2iy + 3x + 3y = 0 The solution to this equation could not be determined.
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