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Simplifying -1i + -2 + -1(4 + -6i) + -1(2 + -7i) = 0 -1i + -2 + (4 * -1 + -6i * -1) + -1(2 + -7i) = 0 -1i + -2 + (-4 + 6i) + -1(2 + -7i) = 0 -1i + -2 + -4 + 6i + (2 * -1 + -7i * -1) = 0 -1i + -2 + -4 + 6i + (-2 + 7i) = 0 Reorder the terms: -2 + -4 + -2 + -1i + 6i + 7i = 0 Combine like terms: -2 + -4 = -6 -6 + -2 + -1i + 6i + 7i = 0 Combine like terms: -6 + -2 = -8 -8 + -1i + 6i + 7i = 0 Combine like terms: -1i + 6i = 5i -8 + 5i + 7i = 0 Combine like terms: 5i + 7i = 12i -8 + 12i = 0 Solving -8 + 12i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 12i = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 12i = 0 + 8 12i = 0 + 8 Combine like terms: 0 + 8 = 8 12i = 8 Divide each side by '12'. i = 0.6666666667 Simplifying i = 0.6666666667
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