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Simplifying (4 + -3i) + -1(3 + 5i) = 0 Remove parenthesis around (4 + -3i) 4 + -3i + -1(3 + 5i) = 0 4 + -3i + (3 * -1 + 5i * -1) = 0 4 + -3i + (-3 + -5i) = 0 Reorder the terms: 4 + -3 + -3i + -5i = 0 Combine like terms: 4 + -3 = 1 1 + -3i + -5i = 0 Combine like terms: -3i + -5i = -8i 1 + -8i = 0 Solving 1 + -8i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -8i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8i = 0 + -1 -8i = 0 + -1 Combine like terms: 0 + -1 = -1 -8i = -1 Divide each side by '-8'. i = 0.125 Simplifying i = 0.125
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