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Simplifying (5 + -6i) + -1(3 + -7i) = 0 Remove parenthesis around (5 + -6i) 5 + -6i + -1(3 + -7i) = 0 5 + -6i + (3 * -1 + -7i * -1) = 0 5 + -6i + (-3 + 7i) = 0 Reorder the terms: 5 + -3 + -6i + 7i = 0 Combine like terms: 5 + -3 = 2 2 + -6i + 7i = 0 Combine like terms: -6i + 7i = 1i 2 + 1i = 0 Solving 2 + 1i = 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 + 1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 1i = 0 + -2 1i = 0 + -2 Combine like terms: 0 + -2 = -2 1i = -2 Divide each side by '1'. i = -2 Simplifying i = -2
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