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Simplifying [(5 + 3i) + -1(4 + -4i)] + (4 + i) = 0 Remove parenthesis around (5 + 3i) [5 + 3i + -1(4 + -4i)] + (4 + i) = 0 [5 + 3i + (4 * -1 + -4i * -1)] + (4 + i) = 0 [5 + 3i + (-4 + 4i)] + (4 + i) = 0 Reorder the terms: [5 + -4 + 3i + 4i] + (4 + i) = 0 Combine like terms: 5 + -4 = 1 [1 + 3i + 4i] + (4 + i) = 0 Combine like terms: 3i + 4i = 7i [1 + 7i] + (4 + i) = 0 Remove brackets around [1 + 7i] 1 + 7i + (4 + i) = 0 Remove parenthesis around (4 + i) 1 + 7i + 4 + i = 0 Reorder the terms: 1 + 4 + 7i + i = 0 Combine like terms: 1 + 4 = 5 5 + 7i + i = 0 Combine like terms: 7i + i = 8i 5 + 8i = 0 Solving 5 + 8i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8i = 0 + -5 8i = 0 + -5 Combine like terms: 0 + -5 = -5 8i = -5 Divide each side by '8'. i = -0.625 Simplifying i = -0.625
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