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Simplifying (-5 + 7i) + -1(10 + -6i) = 15 + i Remove parenthesis around (-5 + 7i) -5 + 7i + -1(10 + -6i) = 15 + i -5 + 7i + (10 * -1 + -6i * -1) = 15 + i -5 + 7i + (-10 + 6i) = 15 + i Reorder the terms: -5 + -10 + 7i + 6i = 15 + i Combine like terms: -5 + -10 = -15 -15 + 7i + 6i = 15 + i Combine like terms: 7i + 6i = 13i -15 + 13i = 15 + i Solving -15 + 13i = 15 + 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. -15 + 13i + -1i = 15 + i + -1i Combine like terms: 13i + -1i = 12i -15 + 12i = 15 + i + -1i Combine like terms: i + -1i = 0 -15 + 12i = 15 + 0 -15 + 12i = 15 Add '15' to each side of the equation. -15 + 15 + 12i = 15 + 15 Combine like terms: -15 + 15 = 0 0 + 12i = 15 + 15 12i = 15 + 15 Combine like terms: 15 + 15 = 30 12i = 30 Divide each side by '12'. i = 2.5 Simplifying i = 2.5
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