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Simplifying (12 + 7i) + (-8 + -1i) = 0 Remove parenthesis around (12 + 7i) 12 + 7i + (-8 + -1i) = 0 Remove parenthesis around (-8 + -1i) 12 + 7i + -8 + -1i = 0 Reorder the terms: 12 + -8 + 7i + -1i = 0 Combine like terms: 12 + -8 = 4 4 + 7i + -1i = 0 Combine like terms: 7i + -1i = 6i 4 + 6i = 0 Solving 4 + 6i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 6i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6i = 0 + -4 6i = 0 + -4 Combine like terms: 0 + -4 = -4 6i = -4 Divide each side by '6'. i = -0.6666666667 Simplifying i = -0.6666666667
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