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Simplifying (10 + -11i) + -1(1 + -9i) = 0 Remove parenthesis around (10 + -11i) 10 + -11i + -1(1 + -9i) = 0 10 + -11i + (1 * -1 + -9i * -1) = 0 10 + -11i + (-1 + 9i) = 0 Reorder the terms: 10 + -1 + -11i + 9i = 0 Combine like terms: 10 + -1 = 9 9 + -11i + 9i = 0 Combine like terms: -11i + 9i = -2i 9 + -2i = 0 Solving 9 + -2i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2i = 0 + -9 -2i = 0 + -9 Combine like terms: 0 + -9 = -9 -2i = -9 Divide each side by '-2'. i = 4.5 Simplifying i = 4.5
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