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Simplifying i(a + bi) + 2(a + -1bi) = -3i (a * i + bi * i) + 2(a + -1bi) = -3i (ai + bi2) + 2(a + -1bi) = -3i ai + bi2 + (a * 2 + -1bi * 2) = -3i ai + bi2 + (2a + -2bi) = -3i Reorder the terms: 2a + ai + -2bi + bi2 = -3i Solving 2a + ai + -2bi + bi2 = -3i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2bi' to each side of the equation. 2a + ai + -2bi + 2bi + bi2 = 2bi + -3i Combine like terms: -2bi + 2bi = 0 2a + ai + 0 + bi2 = 2bi + -3i 2a + ai + bi2 = 2bi + -3i Add '-1bi2' to each side of the equation. 2a + ai + bi2 + -1bi2 = 2bi + -1bi2 + -3i Combine like terms: bi2 + -1bi2 = 0 2a + ai + 0 = 2bi + -1bi2 + -3i 2a + ai = 2bi + -1bi2 + -3i Reorder the terms: 2a + ai + -2bi + bi2 + 3i = 2bi + -2bi + -1bi2 + bi2 + -3i + 3i Combine like terms: 2bi + -2bi = 0 2a + ai + -2bi + bi2 + 3i = 0 + -1bi2 + bi2 + -3i + 3i 2a + ai + -2bi + bi2 + 3i = -1bi2 + bi2 + -3i + 3i Combine like terms: -1bi2 + bi2 = 0 2a + ai + -2bi + bi2 + 3i = 0 + -3i + 3i 2a + ai + -2bi + bi2 + 3i = -3i + 3i Combine like terms: -3i + 3i = 0 2a + ai + -2bi + bi2 + 3i = 0 The solution to this equation could not be determined.
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