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Simplifying (3 + 2i) + (2 + bi) = 5 + -4i Remove parenthesis around (3 + 2i) 3 + 2i + (2 + bi) = 5 + -4i Remove parenthesis around (2 + bi) 3 + 2i + 2 + bi = 5 + -4i Reorder the terms: 3 + 2 + bi + 2i = 5 + -4i Combine like terms: 3 + 2 = 5 5 + bi + 2i = 5 + -4i Add '-5' to each side of the equation. 5 + bi + -5 + 2i = 5 + -5 + -4i Reorder the terms: 5 + -5 + bi + 2i = 5 + -5 + -4i Combine like terms: 5 + -5 = 0 0 + bi + 2i = 5 + -5 + -4i bi + 2i = 5 + -5 + -4i Combine like terms: 5 + -5 = 0 bi + 2i = 0 + -4i bi + 2i = -4i Solving bi + 2i = -4i 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 = -4i + -2i Combine like terms: 2i + -2i = 0 bi + 0 = -4i + -2i bi = -4i + -2i Combine like terms: -4i + -2i = -6i bi = -6i Divide each side by 'i'. b = -6 Simplifying b = -6
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