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Simplifying (5 + -3i) + -1(9 + -2i) = 0 Remove parenthesis around (5 + -3i) 5 + -3i + -1(9 + -2i) = 0 5 + -3i + (9 * -1 + -2i * -1) = 0 5 + -3i + (-9 + 2i) = 0 Reorder the terms: 5 + -9 + -3i + 2i = 0 Combine like terms: 5 + -9 = -4 -4 + -3i + 2i = 0 Combine like terms: -3i + 2i = -1i -4 + -1i = 0 Solving -4 + -1i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1i = 0 + 4 -1i = 0 + 4 Combine like terms: 0 + 4 = 4 -1i = 4 Divide each side by '-1'. i = -4 Simplifying i = -4
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