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Simplifying (10 + -3i) + -1(8 + 3i) = 0 Remove parenthesis around (10 + -3i) 10 + -3i + -1(8 + 3i) = 0 10 + -3i + (8 * -1 + 3i * -1) = 0 10 + -3i + (-8 + -3i) = 0 Reorder the terms: 10 + -8 + -3i + -3i = 0 Combine like terms: 10 + -8 = 2 2 + -3i + -3i = 0 Combine like terms: -3i + -3i = -6i 2 + -6i = 0 Solving 2 + -6i = 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 + -6i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6i = 0 + -2 -6i = 0 + -2 Combine like terms: 0 + -2 = -2 -6i = -2 Divide each side by '-6'. i = 0.3333333333 Simplifying i = 0.3333333333
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