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Simplifying a + bi + 6(a + -1bi) = 7 a + bi + (a * 6 + -1bi * 6) = 7 a + bi + (6a + -6bi) = 7 Reorder the terms: a + 6a + bi + -6bi = 7 Combine like terms: a + 6a = 7a 7a + bi + -6bi = 7 Combine like terms: bi + -6bi = -5bi 7a + -5bi = 7 Solving 7a + -5bi = 7 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5bi' to each side of the equation. 7a + -5bi + 5bi = 7 + 5bi Combine like terms: -5bi + 5bi = 0 7a + 0 = 7 + 5bi 7a = 7 + 5bi Divide each side by '7'. a = 1 + 0.7142857143bi Simplifying a = 1 + 0.7142857143bi
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