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Simplifying A + 3b + (3a + -1b) * I = b + bi Reorder the terms for easier multiplication: A + 3b + I(3a + -1b) = b + bi A + 3b + (3a * I + -1b * I) = b + bi A + 3b + (3aI + -1bI) = b + bi Reorder the terms: A + 3aI + 3b + -1bI = b + bi Solving A + 3aI + 3b + -1bI = b + bi Solving for variable 'A'. Move all terms containing A to the left, all other terms to the right. Add '-3aI' to each side of the equation. A + 3aI + 3b + -3aI + -1bI = b + -3aI + bi Reorder the terms: A + 3aI + -3aI + 3b + -1bI = b + -3aI + bi Combine like terms: 3aI + -3aI = 0 A + 0 + 3b + -1bI = b + -3aI + bi A + 3b + -1bI = b + -3aI + bi Reorder the terms: A + 3b + -1bI = -3aI + b + bi Add '-3b' to each side of the equation. A + 3b + -3b + -1bI = -3aI + b + -3b + bi Combine like terms: 3b + -3b = 0 A + 0 + -1bI = -3aI + b + -3b + bi A + -1bI = -3aI + b + -3b + bi Combine like terms: b + -3b = -2b A + -1bI = -3aI + -2b + bi Add 'bI' to each side of the equation. A + -1bI + bI = -3aI + -2b + bI + bi Combine like terms: -1bI + bI = 0 A + 0 = -3aI + -2b + bI + bi A = -3aI + -2b + bI + bi Simplifying A = -3aI + -2b + bI + bi
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