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Simplifying (3x + 5y) + -1(x + 3y) * i = -2 + 10i Remove parenthesis around (3x + 5y) 3x + 5y + -1(x + 3y) * i = -2 + 10i Reorder the terms for easier multiplication: 3x + 5y + -1i(x + 3y) = -2 + 10i 3x + 5y + (x * -1i + 3y * -1i) = -2 + 10i 3x + 5y + (-1ix + -3iy) = -2 + 10i Reorder the terms: -1ix + -3iy + 3x + 5y = -2 + 10i Solving -1ix + -3iy + 3x + 5y = -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 + -3iy + 3x + -10i + 5y = -2 + 10i + -10i Reorder the terms: -10i + -1ix + -3iy + 3x + 5y = -2 + 10i + -10i Combine like terms: 10i + -10i = 0 -10i + -1ix + -3iy + 3x + 5y = -2 + 0 -10i + -1ix + -3iy + 3x + 5y = -2 Add '-3x' to each side of the equation. -10i + -1ix + -3iy + 3x + -3x + 5y = -2 + -3x Combine like terms: 3x + -3x = 0 -10i + -1ix + -3iy + 0 + 5y = -2 + -3x -10i + -1ix + -3iy + 5y = -2 + -3x Add '-5y' to each side of the equation. -10i + -1ix + -3iy + 5y + -5y = -2 + -3x + -5y Combine like terms: 5y + -5y = 0 -10i + -1ix + -3iy + 0 = -2 + -3x + -5y -10i + -1ix + -3iy = -2 + -3x + -5y Reorder the terms: 2 + -10i + -1ix + -3iy + 3x + 5y = -2 + -3x + -5y + 2 + 3x + 5y Reorder the terms: 2 + -10i + -1ix + -3iy + 3x + 5y = -2 + 2 + -3x + 3x + -5y + 5y Combine like terms: -2 + 2 = 0 2 + -10i + -1ix + -3iy + 3x + 5y = 0 + -3x + 3x + -5y + 5y 2 + -10i + -1ix + -3iy + 3x + 5y = -3x + 3x + -5y + 5y Combine like terms: -3x + 3x = 0 2 + -10i + -1ix + -3iy + 3x + 5y = 0 + -5y + 5y 2 + -10i + -1ix + -3iy + 3x + 5y = -5y + 5y Combine like terms: -5y + 5y = 0 2 + -10i + -1ix + -3iy + 3x + 5y = 0 The solution to this equation could not be determined.
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