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Simplifying (-5 + 7i) + -1(12 + -6i) = -17 + i Remove parenthesis around (-5 + 7i) -5 + 7i + -1(12 + -6i) = -17 + i -5 + 7i + (12 * -1 + -6i * -1) = -17 + i -5 + 7i + (-12 + 6i) = -17 + i Reorder the terms: -5 + -12 + 7i + 6i = -17 + i Combine like terms: -5 + -12 = -17 -17 + 7i + 6i = -17 + i Combine like terms: 7i + 6i = 13i -17 + 13i = -17 + i Add '17' to each side of the equation. -17 + 17 + 13i = -17 + 17 + i Combine like terms: -17 + 17 = 0 0 + 13i = -17 + 17 + i 13i = -17 + 17 + i Combine like terms: -17 + 17 = 0 13i = 0 + i 13i = i Solving 13i = i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1i' to each side of the equation. 13i + -1i = i + -1i Combine like terms: 13i + -1i = 12i 12i = i + -1i Combine like terms: i + -1i = 0 12i = 0 Divide each side by '12'. i = 0 Simplifying i = 0
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