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Simplifying (12 + 9i) + (5 + -2i) = 0 Remove parenthesis around (12 + 9i) 12 + 9i + (5 + -2i) = 0 Remove parenthesis around (5 + -2i) 12 + 9i + 5 + -2i = 0 Reorder the terms: 12 + 5 + 9i + -2i = 0 Combine like terms: 12 + 5 = 17 17 + 9i + -2i = 0 Combine like terms: 9i + -2i = 7i 17 + 7i = 0 Solving 17 + 7i = 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 + 7i = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 7i = 0 + -17 7i = 0 + -17 Combine like terms: 0 + -17 = -17 7i = -17 Divide each side by '7'. i = -2.428571429 Simplifying i = -2.428571429
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