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Simplifying (5 + 3i) + -1(-3 + i) = 0 Remove parenthesis around (5 + 3i) 5 + 3i + -1(-3 + i) = 0 5 + 3i + (-3 * -1 + i * -1) = 0 5 + 3i + (3 + -1i) = 0 Reorder the terms: 5 + 3 + 3i + -1i = 0 Combine like terms: 5 + 3 = 8 8 + 3i + -1i = 0 Combine like terms: 3i + -1i = 2i 8 + 2i = 0 Solving 8 + 2i = 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 + 2i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 2i = 0 + -8 2i = 0 + -8 Combine like terms: 0 + -8 = -8 2i = -8 Divide each side by '2'. i = -4 Simplifying i = -4
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