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Simplifying 6 + -1(-5 + 7i) + -1(-8 + -1i) = 0 6 + (-5 * -1 + 7i * -1) + -1(-8 + -1i) = 0 6 + (5 + -7i) + -1(-8 + -1i) = 0 6 + 5 + -7i + (-8 * -1 + -1i * -1) = 0 6 + 5 + -7i + (8 + 1i) = 0 Reorder the terms: 6 + 5 + 8 + -7i + 1i = 0 Combine like terms: 6 + 5 = 11 11 + 8 + -7i + 1i = 0 Combine like terms: 11 + 8 = 19 19 + -7i + 1i = 0 Combine like terms: -7i + 1i = -6i 19 + -6i = 0 Solving 19 + -6i = 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 + -6i = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -6i = 0 + -19 -6i = 0 + -19 Combine like terms: 0 + -19 = -19 -6i = -19 Divide each side by '-6'. i = 3.166666667 Simplifying i = 3.166666667
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