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Simplifying 3a + (4b + 2) * i = 6i Reorder the terms: 3a + (2 + 4b) * i = 6i Reorder the terms for easier multiplication: 3a + i(2 + 4b) = 6i 3a + (2 * i + 4b * i) = 6i Reorder the terms: 3a + (4bi + 2i) = 6i 3a + (4bi + 2i) = 6i Solving 3a + 4bi + 2i = 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 + 2i = -4bi + 6i Combine like terms: 4bi + -4bi = 0 3a + 0 + 2i = -4bi + 6i 3a + 2i = -4bi + 6i Add '-2i' to each side of the equation. 3a + 2i + -2i = -4bi + 6i + -2i Combine like terms: 2i + -2i = 0 3a + 0 = -4bi + 6i + -2i 3a = -4bi + 6i + -2i Combine like terms: 6i + -2i = 4i 3a = -4bi + 4i Divide each side by '3'. a = -1.333333333bi + 1.333333333i Simplifying a = -1.333333333bi + 1.333333333i
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