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Simplifying 3a + (5 + -2i) * b = 1 + 2i Reorder the terms for easier multiplication: 3a + b(5 + -2i) = 1 + 2i 3a + (5 * b + -2i * b) = 1 + 2i 3a + (5b + -2bi) = 1 + 2i Solving 3a + 5b + -2bi = 1 + 2i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5b' to each side of the equation. 3a + 5b + -5b + -2bi = 1 + -5b + 2i Combine like terms: 5b + -5b = 0 3a + 0 + -2bi = 1 + -5b + 2i 3a + -2bi = 1 + -5b + 2i Add '2bi' to each side of the equation. 3a + -2bi + 2bi = 1 + -5b + 2bi + 2i Combine like terms: -2bi + 2bi = 0 3a + 0 = 1 + -5b + 2bi + 2i 3a = 1 + -5b + 2bi + 2i Divide each side by '3'. a = 0.3333333333 + -1.666666667b + 0.6666666667bi + 0.6666666667i Simplifying a = 0.3333333333 + -1.666666667b + 0.6666666667bi + 0.6666666667i
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