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Simplifying (2 + 3i) + (5 + -2i) = 7 + -1i Remove parenthesis around (2 + 3i) 2 + 3i + (5 + -2i) = 7 + -1i Remove parenthesis around (5 + -2i) 2 + 3i + 5 + -2i = 7 + -1i Reorder the terms: 2 + 5 + 3i + -2i = 7 + -1i Combine like terms: 2 + 5 = 7 7 + 3i + -2i = 7 + -1i Combine like terms: 3i + -2i = 1i 7 + 1i = 7 + -1i Add '-7' to each side of the equation. 7 + -7 + 1i = 7 + -7 + -1i Combine like terms: 7 + -7 = 0 0 + 1i = 7 + -7 + -1i 1i = 7 + -7 + -1i Combine like terms: 7 + -7 = 0 1i = 0 + -1i 1i = -1i Solving 1i = -1i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i' to each side of the equation. 1i + i = -1i + i Combine like terms: 1i + i = 2i 2i = -1i + i Combine like terms: -1i + i = 0 2i = 0 Divide each side by '2'. i = 0 Simplifying i = 0
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