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Simplifying (5 + 3i) + -1(2 + -1i) = 0 Remove parenthesis around (5 + 3i) 5 + 3i + -1(2 + -1i) = 0 5 + 3i + (2 * -1 + -1i * -1) = 0 5 + 3i + (-2 + 1i) = 0 Reorder the terms: 5 + -2 + 3i + 1i = 0 Combine like terms: 5 + -2 = 3 3 + 3i + 1i = 0 Combine like terms: 3i + 1i = 4i 3 + 4i = 0 Solving 3 + 4i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4i = 0 + -3 4i = 0 + -3 Combine like terms: 0 + -3 = -3 4i = -3 Divide each side by '4'. i = -0.75 Simplifying i = -0.75
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