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Simplifying (a + b) + (a + -1b) * i = 7 + 2i Remove parenthesis around (a + b) a + b + (a + -1b) * i = 7 + 2i Reorder the terms for easier multiplication: a + b + i(a + -1b) = 7 + 2i a + b + (a * i + -1b * i) = 7 + 2i a + b + (ai + -1bi) = 7 + 2i Reorder the terms: a + ai + b + -1bi = 7 + 2i Solving a + ai + b + -1bi = 7 + 2i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + ai + b + -1b + -1bi = 7 + -1b + 2i Combine like terms: b + -1b = 0 a + ai + 0 + -1bi = 7 + -1b + 2i a + ai + -1bi = 7 + -1b + 2i Add 'bi' to each side of the equation. a + ai + -1bi + bi = 7 + -1b + bi + 2i Combine like terms: -1bi + bi = 0 a + ai + 0 = 7 + -1b + bi + 2i a + ai = 7 + -1b + bi + 2i Reorder the terms: -7 + a + ai + b + -1bi + -2i = 7 + -1b + bi + 2i + -7 + b + -1bi + -2i Reorder the terms: -7 + a + ai + b + -1bi + -2i = 7 + -7 + -1b + b + bi + -1bi + 2i + -2i Combine like terms: 7 + -7 = 0 -7 + a + ai + b + -1bi + -2i = 0 + -1b + b + bi + -1bi + 2i + -2i -7 + a + ai + b + -1bi + -2i = -1b + b + bi + -1bi + 2i + -2i Combine like terms: -1b + b = 0 -7 + a + ai + b + -1bi + -2i = 0 + bi + -1bi + 2i + -2i -7 + a + ai + b + -1bi + -2i = bi + -1bi + 2i + -2i Combine like terms: bi + -1bi = 0 -7 + a + ai + b + -1bi + -2i = 0 + 2i + -2i -7 + a + ai + b + -1bi + -2i = 2i + -2i Combine like terms: 2i + -2i = 0 -7 + a + ai + b + -1bi + -2i = 0 The solution to this equation could not be determined.
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