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Simplifying -1i + (8 + -2i) + -1(5 + -9i) = 0 Remove parenthesis around (8 + -2i) -1i + 8 + -2i + -1(5 + -9i) = 0 -1i + 8 + -2i + (5 * -1 + -9i * -1) = 0 -1i + 8 + -2i + (-5 + 9i) = 0 Reorder the terms: 8 + -5 + -1i + -2i + 9i = 0 Combine like terms: 8 + -5 = 3 3 + -1i + -2i + 9i = 0 Combine like terms: -1i + -2i = -3i 3 + -3i + 9i = 0 Combine like terms: -3i + 9i = 6i 3 + 6i = 0 Solving 3 + 6i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 6i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 6i = 0 + -3 6i = 0 + -3 Combine like terms: 0 + -3 = -3 6i = -3 Divide each side by '6'. i = -0.5 Simplifying i = -0.5
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