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Simplifying (3 + -6i) + -1(4 + 5i) + -1(-3 + i) = 0 Remove parenthesis around (3 + -6i) 3 + -6i + -1(4 + 5i) + -1(-3 + i) = 0 3 + -6i + (4 * -1 + 5i * -1) + -1(-3 + i) = 0 3 + -6i + (-4 + -5i) + -1(-3 + i) = 0 3 + -6i + -4 + -5i + (-3 * -1 + i * -1) = 0 3 + -6i + -4 + -5i + (3 + -1i) = 0 Reorder the terms: 3 + -4 + 3 + -6i + -5i + -1i = 0 Combine like terms: 3 + -4 = -1 -1 + 3 + -6i + -5i + -1i = 0 Combine like terms: -1 + 3 = 2 2 + -6i + -5i + -1i = 0 Combine like terms: -6i + -5i = -11i 2 + -11i + -1i = 0 Combine like terms: -11i + -1i = -12i 2 + -12i = 0 Solving 2 + -12i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -12i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -12i = 0 + -2 -12i = 0 + -2 Combine like terms: 0 + -2 = -2 -12i = -2 Divide each side by '-12'. i = 0.1666666667 Simplifying i = 0.1666666667
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