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Simplifying (1 + -6i) + -1(2 + 2i) + -1(-7 + i) = 0 Remove parenthesis around (1 + -6i) 1 + -6i + -1(2 + 2i) + -1(-7 + i) = 0 1 + -6i + (2 * -1 + 2i * -1) + -1(-7 + i) = 0 1 + -6i + (-2 + -2i) + -1(-7 + i) = 0 1 + -6i + -2 + -2i + (-7 * -1 + i * -1) = 0 1 + -6i + -2 + -2i + (7 + -1i) = 0 Reorder the terms: 1 + -2 + 7 + -6i + -2i + -1i = 0 Combine like terms: 1 + -2 = -1 -1 + 7 + -6i + -2i + -1i = 0 Combine like terms: -1 + 7 = 6 6 + -6i + -2i + -1i = 0 Combine like terms: -6i + -2i = -8i 6 + -8i + -1i = 0 Combine like terms: -8i + -1i = -9i 6 + -9i = 0 Solving 6 + -9i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -9i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -9i = 0 + -6 -9i = 0 + -6 Combine like terms: 0 + -6 = -6 -9i = -6 Divide each side by '-9'. i = 0.6666666667 Simplifying i = 0.6666666667
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