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Simplifying (X + 4) + (2x + -1y) * I = 9 + 7i Reorder the terms: (4 + X) + (2x + -1y) * I = 9 + 7i Remove parenthesis around (4 + X) 4 + X + (2x + -1y) * I = 9 + 7i Reorder the terms for easier multiplication: 4 + X + I(2x + -1y) = 9 + 7i 4 + X + (2x * I + -1y * I) = 9 + 7i 4 + X + (2xI + -1yI) = 9 + 7i Solving 4 + X + 2xI + -1yI = 9 + 7i Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + X + 2xI + -4 + -1yI = 9 + -4 + 7i Reorder the terms: 4 + -4 + X + 2xI + -1yI = 9 + -4 + 7i Combine like terms: 4 + -4 = 0 0 + X + 2xI + -1yI = 9 + -4 + 7i X + 2xI + -1yI = 9 + -4 + 7i Combine like terms: 9 + -4 = 5 X + 2xI + -1yI = 5 + 7i Add '-2xI' to each side of the equation. X + 2xI + -2xI + -1yI = 5 + 7i + -2xI Combine like terms: 2xI + -2xI = 0 X + 0 + -1yI = 5 + 7i + -2xI X + -1yI = 5 + 7i + -2xI Add 'yI' to each side of the equation. X + -1yI + yI = 5 + 7i + -2xI + yI Combine like terms: -1yI + yI = 0 X + 0 = 5 + 7i + -2xI + yI X = 5 + 7i + -2xI + yI Simplifying X = 5 + 7i + -2xI + yI
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