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Simplifying -3 + 6i + -1(-5 + -3i) + -8i = 0 -3 + 6i + (-5 * -1 + -3i * -1) + -8i = 0 -3 + 6i + (5 + 3i) + -8i = 0 Reorder the terms: -3 + 5 + 6i + 3i + -8i = 0 Combine like terms: -3 + 5 = 2 2 + 6i + 3i + -8i = 0 Combine like terms: 6i + 3i = 9i 2 + 9i + -8i = 0 Combine like terms: 9i + -8i = 1i 2 + 1i = 0 Solving 2 + 1i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1i = 0 + -2 1i = 0 + -2 Combine like terms: 0 + -2 = -2 1i = -2 Divide each side by '1'. i = -2 Simplifying i = -2
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