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Simplifying -4(-5 + -2i) + 5(-1 + -1i) = 0 (-5 * -4 + -2i * -4) + 5(-1 + -1i) = 0 (20 + 8i) + 5(-1 + -1i) = 0 20 + 8i + (-1 * 5 + -1i * 5) = 0 20 + 8i + (-5 + -5i) = 0 Reorder the terms: 20 + -5 + 8i + -5i = 0 Combine like terms: 20 + -5 = 15 15 + 8i + -5i = 0 Combine like terms: 8i + -5i = 3i 15 + 3i = 0 Solving 15 + 3i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 3i = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 3i = 0 + -15 3i = 0 + -15 Combine like terms: 0 + -15 = -15 3i = -15 Divide each side by '3'. i = -5 Simplifying i = -5
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