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Simplifying (5 + 7i) + -1(6 + 5i) + (10 + 5i) = 0 Remove parenthesis around (5 + 7i) 5 + 7i + -1(6 + 5i) + (10 + 5i) = 0 5 + 7i + (6 * -1 + 5i * -1) + (10 + 5i) = 0 5 + 7i + (-6 + -5i) + (10 + 5i) = 0 Remove parenthesis around (10 + 5i) 5 + 7i + -6 + -5i + 10 + 5i = 0 Reorder the terms: 5 + -6 + 10 + 7i + -5i + 5i = 0 Combine like terms: 5 + -6 = -1 -1 + 10 + 7i + -5i + 5i = 0 Combine like terms: -1 + 10 = 9 9 + 7i + -5i + 5i = 0 Combine like terms: 7i + -5i = 2i 9 + 2i + 5i = 0 Combine like terms: 2i + 5i = 7i 9 + 7i = 0 Solving 9 + 7i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 7i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 7i = 0 + -9 7i = 0 + -9 Combine like terms: 0 + -9 = -9 7i = -9 Divide each side by '7'. i = -1.285714286 Simplifying i = -1.285714286
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