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