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Simplifying (5 + 3i) + -1(4 + 5i) = 0 Remove parenthesis around (5 + 3i) 5 + 3i + -1(4 + 5i) = 0 5 + 3i + (4 * -1 + 5i * -1) = 0 5 + 3i + (-4 + -5i) = 0 Reorder the terms: 5 + -4 + 3i + -5i = 0 Combine like terms: 5 + -4 = 1 1 + 3i + -5i = 0 Combine like terms: 3i + -5i = -2i 1 + -2i = 0 Solving 1 + -2i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2i = 0 + -1 -2i = 0 + -1 Combine like terms: 0 + -1 = -1 -2i = -1 Divide each side by '-2'. i = 0.5 Simplifying i = 0.5
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