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Simplifying (10 + 7i) + -1(-5 + 3i) = 0 Remove parenthesis around (10 + 7i) 10 + 7i + -1(-5 + 3i) = 0 10 + 7i + (-5 * -1 + 3i * -1) = 0 10 + 7i + (5 + -3i) = 0 Reorder the terms: 10 + 5 + 7i + -3i = 0 Combine like terms: 10 + 5 = 15 15 + 7i + -3i = 0 Combine like terms: 7i + -3i = 4i 15 + 4i = 0 Solving 15 + 4i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 4i = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 4i = 0 + -15 4i = 0 + -15 Combine like terms: 0 + -15 = -15 4i = -15 Divide each side by '4'. i = -3.75 Simplifying i = -3.75
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