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Simplifying 8 + -1(-2 + 8i) + -1(-7 + -1i) = 0 8 + (-2 * -1 + 8i * -1) + -1(-7 + -1i) = 0 8 + (2 + -8i) + -1(-7 + -1i) = 0 8 + 2 + -8i + (-7 * -1 + -1i * -1) = 0 8 + 2 + -8i + (7 + 1i) = 0 Reorder the terms: 8 + 2 + 7 + -8i + 1i = 0 Combine like terms: 8 + 2 = 10 10 + 7 + -8i + 1i = 0 Combine like terms: 10 + 7 = 17 17 + -8i + 1i = 0 Combine like terms: -8i + 1i = -7i 17 + -7i = 0 Solving 17 + -7i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + -7i = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -7i = 0 + -17 -7i = 0 + -17 Combine like terms: 0 + -17 = -17 -7i = -17 Divide each side by '-7'. i = 2.428571429 Simplifying i = 2.428571429
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