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Simplifying (4 + -4i) + (-1 + 6i) + (i) = 0 Remove parenthesis around (4 + -4i) 4 + -4i + (-1 + 6i) + (i) = 0 Remove parenthesis around (-1 + 6i) 4 + -4i + -1 + 6i + (i) = 0 4 + -4i + -1 + 6i + i = 0 Reorder the terms: 4 + -1 + -4i + 6i + i = 0 Combine like terms: 4 + -1 = 3 3 + -4i + 6i + i = 0 Combine like terms: -4i + 6i = 2i 3 + 2i + i = 0 Combine like terms: 2i + i = 3i 3 + 3i = 0 Solving 3 + 3i = 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 + 3i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3i = 0 + -3 3i = 0 + -3 Combine like terms: 0 + -3 = -3 3i = -3 Divide each side by '3'. i = -1 Simplifying i = -1
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