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Simplifying -3(-3 + -1i) + -1(2 + -4i) = 0 (-3 * -3 + -1i * -3) + -1(2 + -4i) = 0 (9 + 3i) + -1(2 + -4i) = 0 9 + 3i + (2 * -1 + -4i * -1) = 0 9 + 3i + (-2 + 4i) = 0 Reorder the terms: 9 + -2 + 3i + 4i = 0 Combine like terms: 9 + -2 = 7 7 + 3i + 4i = 0 Combine like terms: 3i + 4i = 7i 7 + 7i = 0 Solving 7 + 7i = 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 + 7i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 7i = 0 + -7 7i = 0 + -7 Combine like terms: 0 + -7 = -7 7i = -7 Divide each side by '7'. i = -1 Simplifying i = -1
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