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Simplifying (1 + -5i) + -1(2 + 3i) + -1(-6 + i) = 0 Remove parenthesis around (1 + -5i) 1 + -5i + -1(2 + 3i) + -1(-6 + i) = 0 1 + -5i + (2 * -1 + 3i * -1) + -1(-6 + i) = 0 1 + -5i + (-2 + -3i) + -1(-6 + i) = 0 1 + -5i + -2 + -3i + (-6 * -1 + i * -1) = 0 1 + -5i + -2 + -3i + (6 + -1i) = 0 Reorder the terms: 1 + -2 + 6 + -5i + -3i + -1i = 0 Combine like terms: 1 + -2 = -1 -1 + 6 + -5i + -3i + -1i = 0 Combine like terms: -1 + 6 = 5 5 + -5i + -3i + -1i = 0 Combine like terms: -5i + -3i = -8i 5 + -8i + -1i = 0 Combine like terms: -8i + -1i = -9i 5 + -9i = 0 Solving 5 + -9i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -9i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9i = 0 + -5 -9i = 0 + -5 Combine like terms: 0 + -5 = -5 -9i = -5 Divide each side by '-9'. i = 0.5555555556 Simplifying i = 0.5555555556
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