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Simplifying (a + -1bi)((a + bi) + 1) = 11 + 3i Remove parenthesis around (a + bi) (a + -1bi)(a + bi + 1) = 11 + 3i Reorder the terms: (a + -1bi)(1 + a + bi) = 11 + 3i Multiply (a + -1bi) * (1 + a + bi) (a(1 + a + bi) + -1bi * (1 + a + bi)) = 11 + 3i ((1 * a + a * a + bi * a) + -1bi * (1 + a + bi)) = 11 + 3i Reorder the terms: ((1a + abi + a2) + -1bi * (1 + a + bi)) = 11 + 3i ((1a + abi + a2) + -1bi * (1 + a + bi)) = 11 + 3i (1a + abi + a2 + (1 * -1bi + a * -1bi + bi * -1bi)) = 11 + 3i Reorder the terms: (1a + abi + a2 + (-1abi + -1bi + -1b2i2)) = 11 + 3i (1a + abi + a2 + (-1abi + -1bi + -1b2i2)) = 11 + 3i Reorder the terms: (1a + abi + -1abi + a2 + -1bi + -1b2i2) = 11 + 3i Combine like terms: abi + -1abi = 0 (1a + 0 + a2 + -1bi + -1b2i2) = 11 + 3i (1a + a2 + -1bi + -1b2i2) = 11 + 3i Solving 1a + a2 + -1bi + -1b2i2 = 11 + 3i Solving for variable 'a'. Reorder the terms: -11 + 1a + a2 + -1bi + -1b2i2 + -3i = 11 + 3i + -11 + -3i Reorder the terms: -11 + 1a + a2 + -1bi + -1b2i2 + -3i = 11 + -11 + 3i + -3i Combine like terms: 11 + -11 = 0 -11 + 1a + a2 + -1bi + -1b2i2 + -3i = 0 + 3i + -3i -11 + 1a + a2 + -1bi + -1b2i2 + -3i = 3i + -3i Combine like terms: 3i + -3i = 0 -11 + 1a + a2 + -1bi + -1b2i2 + -3i = 0 The solution to this equation could not be determined.
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