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Simplifying (3 + 2i) + (4 + i) = 7 + -5i Remove parenthesis around (3 + 2i) 3 + 2i + (4 + i) = 7 + -5i Remove parenthesis around (4 + i) 3 + 2i + 4 + i = 7 + -5i Reorder the terms: 3 + 4 + 2i + i = 7 + -5i Combine like terms: 3 + 4 = 7 7 + 2i + i = 7 + -5i Combine like terms: 2i + i = 3i 7 + 3i = 7 + -5i Add '-7' to each side of the equation. 7 + -7 + 3i = 7 + -7 + -5i Combine like terms: 7 + -7 = 0 0 + 3i = 7 + -7 + -5i 3i = 7 + -7 + -5i Combine like terms: 7 + -7 = 0 3i = 0 + -5i 3i = -5i Solving 3i = -5i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '5i' to each side of the equation. 3i + 5i = -5i + 5i Combine like terms: 3i + 5i = 8i 8i = -5i + 5i Combine like terms: -5i + 5i = 0 8i = 0 Divide each side by '8'. i = 0 Simplifying i = 0
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