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Simplifying (4x + 9y + -3) + i(2x + -7y + -3) = 10i Reorder the terms: (-3 + 4x + 9y) + i(2x + -7y + -3) = 10i Remove parenthesis around (-3 + 4x + 9y) -3 + 4x + 9y + i(2x + -7y + -3) = 10i Reorder the terms: -3 + 4x + 9y + i(-3 + 2x + -7y) = 10i -3 + 4x + 9y + (-3 * i + 2x * i + -7y * i) = 10i -3 + 4x + 9y + (-3i + 2ix + -7iy) = 10i Reorder the terms: -3 + -3i + 2ix + -7iy + 4x + 9y = 10i Solving -3 + -3i + 2ix + -7iy + 4x + 9y = 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. -3 + -3i + 2ix + -7iy + 4x + -10i + 9y = 10i + -10i Reorder the terms: -3 + -3i + -10i + 2ix + -7iy + 4x + 9y = 10i + -10i Combine like terms: -3i + -10i = -13i -3 + -13i + 2ix + -7iy + 4x + 9y = 10i + -10i Combine like terms: 10i + -10i = 0 -3 + -13i + 2ix + -7iy + 4x + 9y = 0 Add '3' to each side of the equation. -3 + -13i + 2ix + -7iy + 4x + 3 + 9y = 0 + 3 Reorder the terms: -3 + 3 + -13i + 2ix + -7iy + 4x + 9y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -13i + 2ix + -7iy + 4x + 9y = 0 + 3 -13i + 2ix + -7iy + 4x + 9y = 0 + 3 Combine like terms: 0 + 3 = 3 -13i + 2ix + -7iy + 4x + 9y = 3 Add '-4x' to each side of the equation. -13i + 2ix + -7iy + 4x + -4x + 9y = 3 + -4x Combine like terms: 4x + -4x = 0 -13i + 2ix + -7iy + 0 + 9y = 3 + -4x -13i + 2ix + -7iy + 9y = 3 + -4x Add '-9y' to each side of the equation. -13i + 2ix + -7iy + 9y + -9y = 3 + -4x + -9y Combine like terms: 9y + -9y = 0 -13i + 2ix + -7iy + 0 = 3 + -4x + -9y -13i + 2ix + -7iy = 3 + -4x + -9y Reorder the terms: -3 + -13i + 2ix + -7iy + 4x + 9y = 3 + -4x + -9y + -3 + 4x + 9y Reorder the terms: -3 + -13i + 2ix + -7iy + 4x + 9y = 3 + -3 + -4x + 4x + -9y + 9y Combine like terms: 3 + -3 = 0 -3 + -13i + 2ix + -7iy + 4x + 9y = 0 + -4x + 4x + -9y + 9y -3 + -13i + 2ix + -7iy + 4x + 9y = -4x + 4x + -9y + 9y Combine like terms: -4x + 4x = 0 -3 + -13i + 2ix + -7iy + 4x + 9y = 0 + -9y + 9y -3 + -13i + 2ix + -7iy + 4x + 9y = -9y + 9y Combine like terms: -9y + 9y = 0 -3 + -13i + 2ix + -7iy + 4x + 9y = 0 The solution to this equation could not be determined.
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