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Simplifying (4 + -5i) + -1(8 + -3i) + (-4 + 5i) = 0 Remove parenthesis around (4 + -5i) 4 + -5i + -1(8 + -3i) + (-4 + 5i) = 0 4 + -5i + (8 * -1 + -3i * -1) + (-4 + 5i) = 0 4 + -5i + (-8 + 3i) + (-4 + 5i) = 0 Remove parenthesis around (-4 + 5i) 4 + -5i + -8 + 3i + -4 + 5i = 0 Reorder the terms: 4 + -8 + -4 + -5i + 3i + 5i = 0 Combine like terms: 4 + -8 = -4 -4 + -4 + -5i + 3i + 5i = 0 Combine like terms: -4 + -4 = -8 -8 + -5i + 3i + 5i = 0 Combine like terms: -5i + 3i = -2i -8 + -2i + 5i = 0 Combine like terms: -2i + 5i = 3i -8 + 3i = 0 Solving -8 + 3i = 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 + 3i = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3i = 0 + 8 3i = 0 + 8 Combine like terms: 0 + 8 = 8 3i = 8 Divide each side by '3'. i = 2.666666667 Simplifying i = 2.666666667
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