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Simplifying (4 + -5i) + (8 + 2i) = 0 Remove parenthesis around (4 + -5i) 4 + -5i + (8 + 2i) = 0 Remove parenthesis around (8 + 2i) 4 + -5i + 8 + 2i = 0 Reorder the terms: 4 + 8 + -5i + 2i = 0 Combine like terms: 4 + 8 = 12 12 + -5i + 2i = 0 Combine like terms: -5i + 2i = -3i 12 + -3i = 0 Solving 12 + -3i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -3i = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -3i = 0 + -12 -3i = 0 + -12 Combine like terms: 0 + -12 = -12 -3i = -12 Divide each side by '-3'. i = 4 Simplifying i = 4
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