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Simplifying (12 + 9i) + -1(-5 + -3i) = 0 Remove parenthesis around (12 + 9i) 12 + 9i + -1(-5 + -3i) = 0 12 + 9i + (-5 * -1 + -3i * -1) = 0 12 + 9i + (5 + 3i) = 0 Reorder the terms: 12 + 5 + 9i + 3i = 0 Combine like terms: 12 + 5 = 17 17 + 9i + 3i = 0 Combine like terms: 9i + 3i = 12i 17 + 12i = 0 Solving 17 + 12i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 12i = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 12i = 0 + -17 12i = 0 + -17 Combine like terms: 0 + -17 = -17 12i = -17 Divide each side by '12'. i = -1.416666667 Simplifying i = -1.416666667
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