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Simplifying (3 + -2i)(a + bi) = 18i Multiply (3 + -2i) * (a + bi) (3(a + bi) + -2i * (a + bi)) = 18i ((a * 3 + bi * 3) + -2i * (a + bi)) = 18i ((3a + 3bi) + -2i * (a + bi)) = 18i (3a + 3bi + (a * -2i + bi * -2i)) = 18i (3a + 3bi + (-2ai + -2bi2)) = 18i Reorder the terms: (3a + -2ai + 3bi + -2bi2) = 18i (3a + -2ai + 3bi + -2bi2) = 18i Solving 3a + -2ai + 3bi + -2bi2 = 18i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3bi' to each side of the equation. 3a + -2ai + 3bi + -3bi + -2bi2 = -3bi + 18i Combine like terms: 3bi + -3bi = 0 3a + -2ai + 0 + -2bi2 = -3bi + 18i 3a + -2ai + -2bi2 = -3bi + 18i Add '2bi2' to each side of the equation. 3a + -2ai + -2bi2 + 2bi2 = -3bi + 2bi2 + 18i Combine like terms: -2bi2 + 2bi2 = 0 3a + -2ai + 0 = -3bi + 2bi2 + 18i 3a + -2ai = -3bi + 2bi2 + 18i Reorder the terms: 3a + -2ai + 3bi + -2bi2 + -18i = -3bi + 3bi + 2bi2 + -2bi2 + 18i + -18i Combine like terms: -3bi + 3bi = 0 3a + -2ai + 3bi + -2bi2 + -18i = 0 + 2bi2 + -2bi2 + 18i + -18i 3a + -2ai + 3bi + -2bi2 + -18i = 2bi2 + -2bi2 + 18i + -18i Combine like terms: 2bi2 + -2bi2 = 0 3a + -2ai + 3bi + -2bi2 + -18i = 0 + 18i + -18i 3a + -2ai + 3bi + -2bi2 + -18i = 18i + -18i Combine like terms: 18i + -18i = 0 3a + -2ai + 3bi + -2bi2 + -18i = 0 The solution to this equation could not be determined.
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