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Simplifying (12 + 5i) + -1(7 + 3i) = 0 Remove parenthesis around (12 + 5i) 12 + 5i + -1(7 + 3i) = 0 12 + 5i + (7 * -1 + 3i * -1) = 0 12 + 5i + (-7 + -3i) = 0 Reorder the terms: 12 + -7 + 5i + -3i = 0 Combine like terms: 12 + -7 = 5 5 + 5i + -3i = 0 Combine like terms: 5i + -3i = 2i 5 + 2i = 0 Solving 5 + 2i = 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 + 2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2i = 0 + -5 2i = 0 + -5 Combine like terms: 0 + -5 = -5 2i = -5 Divide each side by '2'. i = -2.5 Simplifying i = -2.5
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