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Simplifying [(3 + 5i) + -1(3 + -2i)] + (8 + i) = 0 Remove parenthesis around (3 + 5i) [3 + 5i + -1(3 + -2i)] + (8 + i) = 0 [3 + 5i + (3 * -1 + -2i * -1)] + (8 + i) = 0 [3 + 5i + (-3 + 2i)] + (8 + i) = 0 Reorder the terms: [3 + -3 + 5i + 2i] + (8 + i) = 0 Combine like terms: 3 + -3 = 0 [0 + 5i + 2i] + (8 + i) = 0 [5i + 2i] + (8 + i) = 0 Combine like terms: 5i + 2i = 7i [7i] + (8 + i) = 0 [7i] + (8 + i) = 0 Remove parenthesis around (8 + i) [7i] + 8 + i = 0 Reorder the terms: 8 + [7i] + i = 0 Combine like terms: [7i] + i = 8i 8 + 8i = 0 Solving 8 + 8i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 8i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 8i = 0 + -8 8i = 0 + -8 Combine like terms: 0 + -8 = -8 8i = -8 Divide each side by '8'. i = -1 Simplifying i = -1
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