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Simplifying (3 + 2i) + (9 + -3i) = 0 Remove parenthesis around (3 + 2i) 3 + 2i + (9 + -3i) = 0 Remove parenthesis around (9 + -3i) 3 + 2i + 9 + -3i = 0 Reorder the terms: 3 + 9 + 2i + -3i = 0 Combine like terms: 3 + 9 = 12 12 + 2i + -3i = 0 Combine like terms: 2i + -3i = -1i 12 + -1i = 0 Solving 12 + -1i = 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 + -1i = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1i = 0 + -12 -1i = 0 + -12 Combine like terms: 0 + -12 = -12 -1i = -12 Divide each side by '-1'. i = 12 Simplifying i = 12
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