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Simplifying (2 + 7i) + -1(5 + -3i) = 0 Remove parenthesis around (2 + 7i) 2 + 7i + -1(5 + -3i) = 0 2 + 7i + (5 * -1 + -3i * -1) = 0 2 + 7i + (-5 + 3i) = 0 Reorder the terms: 2 + -5 + 7i + 3i = 0 Combine like terms: 2 + -5 = -3 -3 + 7i + 3i = 0 Combine like terms: 7i + 3i = 10i -3 + 10i = 0 Solving -3 + 10i = 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 + 10i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 10i = 0 + 3 10i = 0 + 3 Combine like terms: 0 + 3 = 3 10i = 3 Divide each side by '10'. i = 0.3 Simplifying i = 0.3
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