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Simplifying (-5i) + (8 + 2i) + -1(1 + 3i) = 0 Remove parenthesis around (8 + 2i) (-5i) + 8 + 2i + -1(1 + 3i) = 0 (-5i) + 8 + 2i + (1 * -1 + 3i * -1) = 0 (-5i) + 8 + 2i + (-1 + -3i) = 0 Reorder the terms: 8 + -1 + (-5i) + 2i + -3i = 0 Combine like terms: 8 + -1 = 7 7 + (-5i) + 2i + -3i = 0 Combine like terms: (-5i) + 2i = -3i 7 + -3i + -3i = 0 Combine like terms: -3i + -3i = -6i 7 + -6i = 0 Solving 7 + -6i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6i = 0 + -7 -6i = 0 + -7 Combine like terms: 0 + -7 = -7 -6i = -7 Divide each side by '-6'. i = 1.166666667 Simplifying i = 1.166666667
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