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Simplifying (5 + 7i) + -1(-5 + i) = 0 Remove parenthesis around (5 + 7i) 5 + 7i + -1(-5 + i) = 0 5 + 7i + (-5 * -1 + i * -1) = 0 5 + 7i + (5 + -1i) = 0 Reorder the terms: 5 + 5 + 7i + -1i = 0 Combine like terms: 5 + 5 = 10 10 + 7i + -1i = 0 Combine like terms: 7i + -1i = 6i 10 + 6i = 0 Solving 10 + 6i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + 6i = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 6i = 0 + -10 6i = 0 + -10 Combine like terms: 0 + -10 = -10 6i = -10 Divide each side by '6'. i = -1.666666667 Simplifying i = -1.666666667
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