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Simplifying (4 + -1i) + -1(4 + -2i) + (2 + 8i) = 0 Remove parenthesis around (4 + -1i) 4 + -1i + -1(4 + -2i) + (2 + 8i) = 0 4 + -1i + (4 * -1 + -2i * -1) + (2 + 8i) = 0 4 + -1i + (-4 + 2i) + (2 + 8i) = 0 Remove parenthesis around (2 + 8i) 4 + -1i + -4 + 2i + 2 + 8i = 0 Reorder the terms: 4 + -4 + 2 + -1i + 2i + 8i = 0 Combine like terms: 4 + -4 = 0 0 + 2 + -1i + 2i + 8i = 0 2 + -1i + 2i + 8i = 0 Combine like terms: -1i + 2i = 1i 2 + 1i + 8i = 0 Combine like terms: 1i + 8i = 9i 2 + 9i = 0 Solving 2 + 9i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 9i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 9i = 0 + -2 9i = 0 + -2 Combine like terms: 0 + -2 = -2 9i = -2 Divide each side by '9'. i = -0.2222222222 Simplifying i = -0.2222222222
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