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Simplifying (3x + 8y) + -1(x + -2y) * i = 10i + -2 Remove parenthesis around (3x + 8y) 3x + 8y + -1(x + -2y) * i = 10i + -2 Reorder the terms for easier multiplication: 3x + 8y + -1i(x + -2y) = 10i + -2 3x + 8y + (x * -1i + -2y * -1i) = 10i + -2 3x + 8y + (-1ix + 2iy) = 10i + -2 Reorder the terms: -1ix + 2iy + 3x + 8y = 10i + -2 Reorder the terms: -1ix + 2iy + 3x + 8y = -2 + 10i Solving -1ix + 2iy + 3x + 8y = -2 + 10i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-10i' to each side of the equation. -1ix + 2iy + 3x + -10i + 8y = -2 + 10i + -10i Reorder the terms: -10i + -1ix + 2iy + 3x + 8y = -2 + 10i + -10i Combine like terms: 10i + -10i = 0 -10i + -1ix + 2iy + 3x + 8y = -2 + 0 -10i + -1ix + 2iy + 3x + 8y = -2 Add '-3x' to each side of the equation. -10i + -1ix + 2iy + 3x + -3x + 8y = -2 + -3x Combine like terms: 3x + -3x = 0 -10i + -1ix + 2iy + 0 + 8y = -2 + -3x -10i + -1ix + 2iy + 8y = -2 + -3x Add '-8y' to each side of the equation. -10i + -1ix + 2iy + 8y + -8y = -2 + -3x + -8y Combine like terms: 8y + -8y = 0 -10i + -1ix + 2iy + 0 = -2 + -3x + -8y -10i + -1ix + 2iy = -2 + -3x + -8y Reorder the terms: 2 + -10i + -1ix + 2iy + 3x + 8y = -2 + -3x + -8y + 2 + 3x + 8y Reorder the terms: 2 + -10i + -1ix + 2iy + 3x + 8y = -2 + 2 + -3x + 3x + -8y + 8y Combine like terms: -2 + 2 = 0 2 + -10i + -1ix + 2iy + 3x + 8y = 0 + -3x + 3x + -8y + 8y 2 + -10i + -1ix + 2iy + 3x + 8y = -3x + 3x + -8y + 8y Combine like terms: -3x + 3x = 0 2 + -10i + -1ix + 2iy + 3x + 8y = 0 + -8y + 8y 2 + -10i + -1ix + 2iy + 3x + 8y = -8y + 8y Combine like terms: -8y + 8y = 0 2 + -10i + -1ix + 2iy + 3x + 8y = 0 The solution to this equation could not be determined.
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