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Simplifying (12 + 6i) + -1(9 + 4i) = 0 Remove parenthesis around (12 + 6i) 12 + 6i + -1(9 + 4i) = 0 12 + 6i + (9 * -1 + 4i * -1) = 0 12 + 6i + (-9 + -4i) = 0 Reorder the terms: 12 + -9 + 6i + -4i = 0 Combine like terms: 12 + -9 = 3 3 + 6i + -4i = 0 Combine like terms: 6i + -4i = 2i 3 + 2i = 0 Solving 3 + 2i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5
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