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Simplifying (5 + -2i) + -1(-4 + -1i) = 0 Remove parenthesis around (5 + -2i) 5 + -2i + -1(-4 + -1i) = 0 5 + -2i + (-4 * -1 + -1i * -1) = 0 5 + -2i + (4 + 1i) = 0 Reorder the terms: 5 + 4 + -2i + 1i = 0 Combine like terms: 5 + 4 = 9 9 + -2i + 1i = 0 Combine like terms: -2i + 1i = -1i 9 + -1i = 0 Solving 9 + -1i = 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 + -1i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1i = 0 + -9 -1i = 0 + -9 Combine like terms: 0 + -9 = -9 -1i = -9 Divide each side by '-1'. i = 9 Simplifying i = 9
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