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Simplifying 3 + -1(-5 + 7i) + -1(-1 + -1i) = 0 3 + (-5 * -1 + 7i * -1) + -1(-1 + -1i) = 0 3 + (5 + -7i) + -1(-1 + -1i) = 0 3 + 5 + -7i + (-1 * -1 + -1i * -1) = 0 3 + 5 + -7i + (1 + 1i) = 0 Reorder the terms: 3 + 5 + 1 + -7i + 1i = 0 Combine like terms: 3 + 5 = 8 8 + 1 + -7i + 1i = 0 Combine like terms: 8 + 1 = 9 9 + -7i + 1i = 0 Combine like terms: -7i + 1i = -6i 9 + -6i = 0 Solving 9 + -6i = 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 + -6i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -6i = 0 + -9 -6i = 0 + -9 Combine like terms: 0 + -9 = -9 -6i = -9 Divide each side by '-6'. i = 1.5 Simplifying i = 1.5
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