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Simplifying i + 3b + (3a + -1b) * i = 6 + 6i Reorder the terms for easier multiplication: i + 3b + i(3a + -1b) = 6 + 6i i + 3b + (3a * i + -1b * i) = 6 + 6i i + 3b + (3ai + -1bi) = 6 + 6i Reorder the terms: 3ai + 3b + -1bi + i = 6 + 6i Solving 3ai + 3b + -1bi + i = 6 + 6i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 3ai + 3b + -1bi + -3b + i = 6 + -3b + 6i Reorder the terms: 3ai + 3b + -3b + -1bi + i = 6 + -3b + 6i Combine like terms: 3b + -3b = 0 3ai + 0 + -1bi + i = 6 + -3b + 6i 3ai + -1bi + i = 6 + -3b + 6i Add 'bi' to each side of the equation. 3ai + -1bi + bi + i = 6 + -3b + bi + 6i Combine like terms: -1bi + bi = 0 3ai + 0 + i = 6 + -3b + bi + 6i 3ai + i = 6 + -3b + bi + 6i Add '-1i' to each side of the equation. 3ai + i + -1i = 6 + -3b + bi + 6i + -1i Combine like terms: i + -1i = 0 3ai + 0 = 6 + -3b + bi + 6i + -1i 3ai = 6 + -3b + bi + 6i + -1i Combine like terms: 6i + -1i = 5i 3ai = 6 + -3b + bi + 5i Divide each side by '3i'. a = 2i-1 + -1bi-1 + 0.3333333333b + 1.666666667 Simplifying a = 2i-1 + -1bi-1 + 0.3333333333b + 1.666666667 Reorder the terms: a = 1.666666667 + 0.3333333333b + -1bi-1 + 2i-1
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