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Simplifying (5 + 4i) + -1(-9 + i) = 0 Remove parenthesis around (5 + 4i) 5 + 4i + -1(-9 + i) = 0 5 + 4i + (-9 * -1 + i * -1) = 0 5 + 4i + (9 + -1i) = 0 Reorder the terms: 5 + 9 + 4i + -1i = 0 Combine like terms: 5 + 9 = 14 14 + 4i + -1i = 0 Combine like terms: 4i + -1i = 3i 14 + 3i = 0 Solving 14 + 3i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 3i = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 3i = 0 + -14 3i = 0 + -14 Combine like terms: 0 + -14 = -14 3i = -14 Divide each side by '3'. i = -4.666666667 Simplifying i = -4.666666667
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