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Simplifying (1 + -6i) + -1(5 + 4i) + -1(-6 + i) = 0 Remove parenthesis around (1 + -6i) 1 + -6i + -1(5 + 4i) + -1(-6 + i) = 0 1 + -6i + (5 * -1 + 4i * -1) + -1(-6 + i) = 0 1 + -6i + (-5 + -4i) + -1(-6 + i) = 0 1 + -6i + -5 + -4i + (-6 * -1 + i * -1) = 0 1 + -6i + -5 + -4i + (6 + -1i) = 0 Reorder the terms: 1 + -5 + 6 + -6i + -4i + -1i = 0 Combine like terms: 1 + -5 = -4 -4 + 6 + -6i + -4i + -1i = 0 Combine like terms: -4 + 6 = 2 2 + -6i + -4i + -1i = 0 Combine like terms: -6i + -4i = -10i 2 + -10i + -1i = 0 Combine like terms: -10i + -1i = -11i 2 + -11i = 0 Solving 2 + -11i = 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 + -11i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -11i = 0 + -2 -11i = 0 + -2 Combine like terms: 0 + -2 = -2 -11i = -2 Divide each side by '-11'. i = 0.1818181818 Simplifying i = 0.1818181818
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