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Simplifying -1i + -4 + -1(6 + -7i) + -1(2 + -5i) = 0 -1i + -4 + (6 * -1 + -7i * -1) + -1(2 + -5i) = 0 -1i + -4 + (-6 + 7i) + -1(2 + -5i) = 0 -1i + -4 + -6 + 7i + (2 * -1 + -5i * -1) = 0 -1i + -4 + -6 + 7i + (-2 + 5i) = 0 Reorder the terms: -4 + -6 + -2 + -1i + 7i + 5i = 0 Combine like terms: -4 + -6 = -10 -10 + -2 + -1i + 7i + 5i = 0 Combine like terms: -10 + -2 = -12 -12 + -1i + 7i + 5i = 0 Combine like terms: -1i + 7i = 6i -12 + 6i + 5i = 0 Combine like terms: 6i + 5i = 11i -12 + 11i = 0 Solving -12 + 11i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + 11i = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 11i = 0 + 12 11i = 0 + 12 Combine like terms: 0 + 12 = 12 11i = 12 Divide each side by '11'. i = 1.090909091 Simplifying i = 1.090909091
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