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Simplifying (10 + 3i) + -1(8 + -16i) + -1(-9 + 13i) = 0 Remove parenthesis around (10 + 3i) 10 + 3i + -1(8 + -16i) + -1(-9 + 13i) = 0 10 + 3i + (8 * -1 + -16i * -1) + -1(-9 + 13i) = 0 10 + 3i + (-8 + 16i) + -1(-9 + 13i) = 0 10 + 3i + -8 + 16i + (-9 * -1 + 13i * -1) = 0 10 + 3i + -8 + 16i + (9 + -13i) = 0 Reorder the terms: 10 + -8 + 9 + 3i + 16i + -13i = 0 Combine like terms: 10 + -8 = 2 2 + 9 + 3i + 16i + -13i = 0 Combine like terms: 2 + 9 = 11 11 + 3i + 16i + -13i = 0 Combine like terms: 3i + 16i = 19i 11 + 19i + -13i = 0 Combine like terms: 19i + -13i = 6i 11 + 6i = 0 Solving 11 + 6i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 6i = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 6i = 0 + -11 6i = 0 + -11 Combine like terms: 0 + -11 = -11 6i = -11 Divide each side by '6'. i = -1.833333333 Simplifying i = -1.833333333
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