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Simplifying 8 + -1(-6 + 8i) + -1(-7 + -1i) = 0 8 + (-6 * -1 + 8i * -1) + -1(-7 + -1i) = 0 8 + (6 + -8i) + -1(-7 + -1i) = 0 8 + 6 + -8i + (-7 * -1 + -1i * -1) = 0 8 + 6 + -8i + (7 + 1i) = 0 Reorder the terms: 8 + 6 + 7 + -8i + 1i = 0 Combine like terms: 8 + 6 = 14 14 + 7 + -8i + 1i = 0 Combine like terms: 14 + 7 = 21 21 + -8i + 1i = 0 Combine like terms: -8i + 1i = -7i 21 + -7i = 0 Solving 21 + -7i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -7i = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -7i = 0 + -21 -7i = 0 + -21 Combine like terms: 0 + -21 = -21 -7i = -21 Divide each side by '-7'. i = 3 Simplifying i = 3
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