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Simplifying 2 + 3ix + -1(4 + 5i) = (4i + -3) * x + -5i 2 + 3ix + (4 * -1 + 5i * -1) = (4i + -3) * x + -5i 2 + 3ix + (-4 + -5i) = (4i + -3) * x + -5i Reorder the terms: 2 + -4 + -5i + 3ix = (4i + -3) * x + -5i Combine like terms: 2 + -4 = -2 -2 + -5i + 3ix = (4i + -3) * x + -5i Reorder the terms: -2 + -5i + 3ix = (-3 + 4i) * x + -5i Reorder the terms for easier multiplication: -2 + -5i + 3ix = x(-3 + 4i) + -5i -2 + -5i + 3ix = (-3 * x + 4i * x) + -5i Reorder the terms: -2 + -5i + 3ix = (4ix + -3x) + -5i -2 + -5i + 3ix = (4ix + -3x) + -5i Reorder the terms: -2 + -5i + 3ix = -5i + 4ix + -3x Add '5i' to each side of the equation. -2 + -5i + 5i + 3ix = -5i + 4ix + 5i + -3x Combine like terms: -5i + 5i = 0 -2 + 0 + 3ix = -5i + 4ix + 5i + -3x -2 + 3ix = -5i + 4ix + 5i + -3x Reorder the terms: -2 + 3ix = -5i + 5i + 4ix + -3x Combine like terms: -5i + 5i = 0 -2 + 3ix = 0 + 4ix + -3x -2 + 3ix = 4ix + -3x Solving -2 + 3ix = 4ix + -3x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4ix' to each side of the equation. -2 + 3ix + -4ix = 4ix + -4ix + -3x Combine like terms: 3ix + -4ix = -1ix -2 + -1ix = 4ix + -4ix + -3x Combine like terms: 4ix + -4ix = 0 -2 + -1ix = 0 + -3x -2 + -1ix = -3x Add '2' to each side of the equation. -2 + 2 + -1ix = 2 + -3x Combine like terms: -2 + 2 = 0 0 + -1ix = 2 + -3x -1ix = 2 + -3x Divide each side by '-1x'. i = -2x-1 + 3 Simplifying i = -2x-1 + 3 Reorder the terms: i = 3 + -2x-1
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