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Simplifying a + 3a + -3bi + bi = 1 + 2i Combine like terms: a + 3a = 4a 4a + -3bi + bi = 1 + 2i Combine like terms: -3bi + bi = -2bi 4a + -2bi = 1 + 2i Solving 4a + -2bi = 1 + 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. 4a + -2bi + 2bi = 1 + 2bi + 2i Combine like terms: -2bi + 2bi = 0 4a + 0 = 1 + 2bi + 2i 4a = 1 + 2bi + 2i Divide each side by '4'. a = 0.25 + 0.5bi + 0.5i Simplifying a = 0.25 + 0.5bi + 0.5i
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