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Simplifying (2b + -1) * i + (a + 3) = 4 + -8i Reorder the terms: (-1 + 2b) * i + (a + 3) = 4 + -8i Reorder the terms for easier multiplication: i(-1 + 2b) + (a + 3) = 4 + -8i (-1 * i + 2b * i) + (a + 3) = 4 + -8i Reorder the terms: (2bi + -1i) + (a + 3) = 4 + -8i (2bi + -1i) + (a + 3) = 4 + -8i Reorder the terms: 2bi + -1i + (3 + a) = 4 + -8i Remove parenthesis around (3 + a) 2bi + -1i + 3 + a = 4 + -8i Reorder the terms: 3 + a + 2bi + -1i = 4 + -8i Solving 3 + a + 2bi + -1i = 4 + -8i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + a + 2bi + -3 + -1i = 4 + -3 + -8i Reorder the terms: 3 + -3 + a + 2bi + -1i = 4 + -3 + -8i Combine like terms: 3 + -3 = 0 0 + a + 2bi + -1i = 4 + -3 + -8i a + 2bi + -1i = 4 + -3 + -8i Combine like terms: 4 + -3 = 1 a + 2bi + -1i = 1 + -8i Add '-2bi' to each side of the equation. a + 2bi + -2bi + -1i = 1 + -2bi + -8i Combine like terms: 2bi + -2bi = 0 a + 0 + -1i = 1 + -2bi + -8i a + -1i = 1 + -2bi + -8i Add 'i' to each side of the equation. a + -1i + i = 1 + -2bi + -8i + i Combine like terms: -1i + i = 0 a + 0 = 1 + -2bi + -8i + i a = 1 + -2bi + -8i + i Combine like terms: -8i + i = -7i a = 1 + -2bi + -7i Simplifying a = 1 + -2bi + -7i
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