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Simplifying (10 + 3i) + -1(i + -16i) + -1(-9 + 13i) = 0 Remove parenthesis around (10 + 3i) 10 + 3i + -1(i + -16i) + -1(-9 + 13i) = 0 Combine like terms: i + -16i = -15i 10 + 3i + -1(-15i) + -1(-9 + 13i) = 0 Remove parenthesis around (-15i) 10 + 3i + -1 * -15i + -1(-9 + 13i) = 0 Multiply -1 * -15 10 + 3i + 15i + -1(-9 + 13i) = 0 10 + 3i + 15i + (-9 * -1 + 13i * -1) = 0 10 + 3i + 15i + (9 + -13i) = 0 Reorder the terms: 10 + 9 + 3i + 15i + -13i = 0 Combine like terms: 10 + 9 = 19 19 + 3i + 15i + -13i = 0 Combine like terms: 3i + 15i = 18i 19 + 18i + -13i = 0 Combine like terms: 18i + -13i = 5i 19 + 5i = 0 Solving 19 + 5i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + 5i = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 5i = 0 + -19 5i = 0 + -19 Combine like terms: 0 + -19 = -19 5i = -19 Divide each side by '5'. i = -3.8 Simplifying i = -3.8
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