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Simplifying 8 + -1(-4 + 7i) + -1(-4 + -1i) = 0 8 + (-4 * -1 + 7i * -1) + -1(-4 + -1i) = 0 8 + (4 + -7i) + -1(-4 + -1i) = 0 8 + 4 + -7i + (-4 * -1 + -1i * -1) = 0 8 + 4 + -7i + (4 + 1i) = 0 Reorder the terms: 8 + 4 + 4 + -7i + 1i = 0 Combine like terms: 8 + 4 = 12 12 + 4 + -7i + 1i = 0 Combine like terms: 12 + 4 = 16 16 + -7i + 1i = 0 Combine like terms: -7i + 1i = -6i 16 + -6i = 0 Solving 16 + -6i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + -6i = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -6i = 0 + -16 -6i = 0 + -16 Combine like terms: 0 + -16 = -16 -6i = -16 Divide each side by '-6'. i = 2.666666667 Simplifying i = 2.666666667
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