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Simplifying (9 + 3i) + -1(6 + 10i) + (1 + 9i) = 0 Remove parenthesis around (9 + 3i) 9 + 3i + -1(6 + 10i) + (1 + 9i) = 0 9 + 3i + (6 * -1 + 10i * -1) + (1 + 9i) = 0 9 + 3i + (-6 + -10i) + (1 + 9i) = 0 Remove parenthesis around (1 + 9i) 9 + 3i + -6 + -10i + 1 + 9i = 0 Reorder the terms: 9 + -6 + 1 + 3i + -10i + 9i = 0 Combine like terms: 9 + -6 = 3 3 + 1 + 3i + -10i + 9i = 0 Combine like terms: 3 + 1 = 4 4 + 3i + -10i + 9i = 0 Combine like terms: 3i + -10i = -7i 4 + -7i + 9i = 0 Combine like terms: -7i + 9i = 2i 4 + 2i = 0 Solving 4 + 2i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 2i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2i = 0 + -4 2i = 0 + -4 Combine like terms: 0 + -4 = -4 2i = -4 Divide each side by '2'. i = -2 Simplifying i = -2
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