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Simplifying 3a + (4b + 3) * i = 9 + -6i Reorder the terms: 3a + (3 + 4b) * i = 9 + -6i Reorder the terms for easier multiplication: 3a + i(3 + 4b) = 9 + -6i 3a + (3 * i + 4b * i) = 9 + -6i Reorder the terms: 3a + (4bi + 3i) = 9 + -6i 3a + (4bi + 3i) = 9 + -6i Solving 3a + 4bi + 3i = 9 + -6i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4bi' to each side of the equation. 3a + 4bi + -4bi + 3i = 9 + -4bi + -6i Combine like terms: 4bi + -4bi = 0 3a + 0 + 3i = 9 + -4bi + -6i 3a + 3i = 9 + -4bi + -6i Add '-3i' to each side of the equation. 3a + 3i + -3i = 9 + -4bi + -6i + -3i Combine like terms: 3i + -3i = 0 3a + 0 = 9 + -4bi + -6i + -3i 3a = 9 + -4bi + -6i + -3i Combine like terms: -6i + -3i = -9i 3a = 9 + -4bi + -9i Divide each side by '3'. a = 3 + -1.333333333bi + -3i Simplifying a = 3 + -1.333333333bi + -3i
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