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Simplifying (a + b)(2 + i) = b + 1 + (10 + 2a) * i Multiply (a + b) * (2 + i) (a(2 + i) + b(2 + i)) = b + 1 + (10 + 2a) * i ((2 * a + i * a) + b(2 + i)) = b + 1 + (10 + 2a) * i ((2a + ai) + b(2 + i)) = b + 1 + (10 + 2a) * i (2a + ai + (2 * b + i * b)) = b + 1 + (10 + 2a) * i (2a + ai + (2b + bi)) = b + 1 + (10 + 2a) * i (2a + ai + 2b + bi) = b + 1 + (10 + 2a) * i Reorder the terms for easier multiplication: 2a + ai + 2b + bi = b + 1 + i(10 + 2a) 2a + ai + 2b + bi = b + 1 + (10 * i + 2a * i) Reorder the terms: 2a + ai + 2b + bi = b + 1 + (2ai + 10i) 2a + ai + 2b + bi = b + 1 + (2ai + 10i) Reorder the terms: 2a + ai + 2b + bi = 1 + 2ai + b + 10i Solving 2a + ai + 2b + bi = 1 + 2ai + b + 10i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2ai' to each side of the equation. 2a + ai + 2b + -2ai + bi = 1 + 2ai + b + -2ai + 10i Reorder the terms: 2a + ai + -2ai + 2b + bi = 1 + 2ai + b + -2ai + 10i Combine like terms: ai + -2ai = -1ai 2a + -1ai + 2b + bi = 1 + 2ai + b + -2ai + 10i Reorder the terms: 2a + -1ai + 2b + bi = 1 + 2ai + -2ai + b + 10i Combine like terms: 2ai + -2ai = 0 2a + -1ai + 2b + bi = 1 + 0 + b + 10i 2a + -1ai + 2b + bi = 1 + b + 10i Add '-2b' to each side of the equation. 2a + -1ai + 2b + -2b + bi = 1 + b + -2b + 10i Combine like terms: 2b + -2b = 0 2a + -1ai + 0 + bi = 1 + b + -2b + 10i 2a + -1ai + bi = 1 + b + -2b + 10i Combine like terms: b + -2b = -1b 2a + -1ai + bi = 1 + -1b + 10i Add '-1bi' to each side of the equation. 2a + -1ai + bi + -1bi = 1 + -1b + -1bi + 10i Combine like terms: bi + -1bi = 0 2a + -1ai + 0 = 1 + -1b + -1bi + 10i 2a + -1ai = 1 + -1b + -1bi + 10i Reorder the terms: -1 + 2a + -1ai + b + bi + -10i = 1 + -1b + -1bi + 10i + -1 + b + bi + -10i Reorder the terms: -1 + 2a + -1ai + b + bi + -10i = 1 + -1 + -1b + b + -1bi + bi + 10i + -10i Combine like terms: 1 + -1 = 0 -1 + 2a + -1ai + b + bi + -10i = 0 + -1b + b + -1bi + bi + 10i + -10i -1 + 2a + -1ai + b + bi + -10i = -1b + b + -1bi + bi + 10i + -10i Combine like terms: -1b + b = 0 -1 + 2a + -1ai + b + bi + -10i = 0 + -1bi + bi + 10i + -10i -1 + 2a + -1ai + b + bi + -10i = -1bi + bi + 10i + -10i Combine like terms: -1bi + bi = 0 -1 + 2a + -1ai + b + bi + -10i = 0 + 10i + -10i -1 + 2a + -1ai + b + bi + -10i = 10i + -10i Combine like terms: 10i + -10i = 0 -1 + 2a + -1ai + b + bi + -10i = 0 The solution to this equation could not be determined.
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