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Simplifying (-5 + 3i) + -1(-8 + 2i) = 0 Remove parenthesis around (-5 + 3i) -5 + 3i + -1(-8 + 2i) = 0 -5 + 3i + (-8 * -1 + 2i * -1) = 0 -5 + 3i + (8 + -2i) = 0 Reorder the terms: -5 + 8 + 3i + -2i = 0 Combine like terms: -5 + 8 = 3 3 + 3i + -2i = 0 Combine like terms: 3i + -2i = 1i 3 + 1i = 0 Solving 3 + 1i = 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 + 1i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 1i = 0 + -3 1i = 0 + -3 Combine like terms: 0 + -3 = -3 1i = -3 Divide each side by '1'. i = -3 Simplifying i = -3
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