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Simplifying (5 + -2i) + (3 + 9i) = 0 Remove parenthesis around (5 + -2i) 5 + -2i + (3 + 9i) = 0 Remove parenthesis around (3 + 9i) 5 + -2i + 3 + 9i = 0 Reorder the terms: 5 + 3 + -2i + 9i = 0 Combine like terms: 5 + 3 = 8 8 + -2i + 9i = 0 Combine like terms: -2i + 9i = 7i 8 + 7i = 0 Solving 8 + 7i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 7i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 7i = 0 + -8 7i = 0 + -8 Combine like terms: 0 + -8 = -8 7i = -8 Divide each side by '7'. i = -1.142857143 Simplifying i = -1.142857143
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