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Simplifying (3 + -2i) + -1(5 + 3i) = 0 Remove parenthesis around (3 + -2i) 3 + -2i + -1(5 + 3i) = 0 3 + -2i + (5 * -1 + 3i * -1) = 0 3 + -2i + (-5 + -3i) = 0 Reorder the terms: 3 + -5 + -2i + -3i = 0 Combine like terms: 3 + -5 = -2 -2 + -2i + -3i = 0 Combine like terms: -2i + -3i = -5i -2 + -5i = 0 Solving -2 + -5i = 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 + -5i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5i = 0 + 2 -5i = 0 + 2 Combine like terms: 0 + 2 = 2 -5i = 2 Divide each side by '-5'. i = -0.4 Simplifying i = -0.4
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