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Simplifying (4 + 5i) + (8 + 5i) + (3 + -2) = 0 Remove parenthesis around (4 + 5i) 4 + 5i + (8 + 5i) + (3 + -2) = 0 Remove parenthesis around (8 + 5i) 4 + 5i + 8 + 5i + (3 + -2) = 0 Combine like terms: 3 + -2 = 1 4 + 5i + 8 + 5i + (1) = 0 4 + 5i + 8 + 5i + 1 = 0 Reorder the terms: 4 + 8 + 1 + 5i + 5i = 0 Combine like terms: 4 + 8 = 12 12 + 1 + 5i + 5i = 0 Combine like terms: 12 + 1 = 13 13 + 5i + 5i = 0 Combine like terms: 5i + 5i = 10i 13 + 10i = 0 Solving 13 + 10i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 10i = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 10i = 0 + -13 10i = 0 + -13 Combine like terms: 0 + -13 = -13 10i = -13 Divide each side by '10'. i = -1.3 Simplifying i = -1.3