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Simplifying 2(a + bi) + -1i(a + -1bi) = 2 + 2i (a * 2 + bi * 2) + -1i(a + -1bi) = 2 + 2i (2a + 2bi) + -1i(a + -1bi) = 2 + 2i 2a + 2bi + (a * -1i + -1bi * -1i) = 2 + 2i 2a + 2bi + (-1ai + 1bi2) = 2 + 2i Reorder the terms: 2a + -1ai + 2bi + 1bi2 = 2 + 2i Solving 2a + -1ai + 2bi + 1bi2 = 2 + 2i 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 + -1ai + 2bi + -2bi + 1bi2 = 2 + -2bi + 2i Combine like terms: 2bi + -2bi = 0 2a + -1ai + 0 + 1bi2 = 2 + -2bi + 2i 2a + -1ai + 1bi2 = 2 + -2bi + 2i Add '-1bi2' to each side of the equation. 2a + -1ai + 1bi2 + -1bi2 = 2 + -2bi + -1bi2 + 2i Combine like terms: 1bi2 + -1bi2 = 0 2a + -1ai + 0 = 2 + -2bi + -1bi2 + 2i 2a + -1ai = 2 + -2bi + -1bi2 + 2i Reorder the terms: -2 + 2a + -1ai + 2bi + bi2 + -2i = 2 + -2bi + -1bi2 + 2i + -2 + 2bi + bi2 + -2i Reorder the terms: -2 + 2a + -1ai + 2bi + bi2 + -2i = 2 + -2 + -2bi + 2bi + -1bi2 + bi2 + 2i + -2i Combine like terms: 2 + -2 = 0 -2 + 2a + -1ai + 2bi + bi2 + -2i = 0 + -2bi + 2bi + -1bi2 + bi2 + 2i + -2i -2 + 2a + -1ai + 2bi + bi2 + -2i = -2bi + 2bi + -1bi2 + bi2 + 2i + -2i Combine like terms: -2bi + 2bi = 0 -2 + 2a + -1ai + 2bi + bi2 + -2i = 0 + -1bi2 + bi2 + 2i + -2i -2 + 2a + -1ai + 2bi + bi2 + -2i = -1bi2 + bi2 + 2i + -2i Combine like terms: -1bi2 + bi2 = 0 -2 + 2a + -1ai + 2bi + bi2 + -2i = 0 + 2i + -2i -2 + 2a + -1ai + 2bi + bi2 + -2i = 2i + -2i Combine like terms: 2i + -2i = 0 -2 + 2a + -1ai + 2bi + bi2 + -2i = 0 The solution to this equation could not be determined.
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