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Simplifying (5 + -3i) + -1(7 + -2i) = 0 Remove parenthesis around (5 + -3i) 5 + -3i + -1(7 + -2i) = 0 5 + -3i + (7 * -1 + -2i * -1) = 0 5 + -3i + (-7 + 2i) = 0 Reorder the terms: 5 + -7 + -3i + 2i = 0 Combine like terms: 5 + -7 = -2 -2 + -3i + 2i = 0 Combine like terms: -3i + 2i = -1i -2 + -1i = 0 Solving -2 + -1i = 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 + -1i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1i = 0 + 2 -1i = 0 + 2 Combine like terms: 0 + 2 = 2 -1i = 2 Divide each side by '-1'. i = -2 Simplifying i = -2
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