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Simplifying (a + bi) + -2(a + -1bi) + 7 + -6i = 0 Remove parenthesis around (a + bi) a + bi + -2(a + -1bi) + 7 + -6i = 0 a + bi + (a * -2 + -1bi * -2) + 7 + -6i = 0 a + bi + (-2a + 2bi) + 7 + -6i = 0 Reorder the terms: 7 + a + -2a + bi + 2bi + -6i = 0 Combine like terms: a + -2a = -1a 7 + -1a + bi + 2bi + -6i = 0 Combine like terms: bi + 2bi = 3bi 7 + -1a + 3bi + -6i = 0 Solving 7 + -1a + 3bi + -6i = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -1a + 3bi + -7 + -6i = 0 + -7 Reorder the terms: 7 + -7 + -1a + 3bi + -6i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1a + 3bi + -6i = 0 + -7 -1a + 3bi + -6i = 0 + -7 Combine like terms: 0 + -7 = -7 -1a + 3bi + -6i = -7 Add '-3bi' to each side of the equation. -1a + 3bi + -3bi + -6i = -7 + -3bi Combine like terms: 3bi + -3bi = 0 -1a + 0 + -6i = -7 + -3bi -1a + -6i = -7 + -3bi Add '6i' to each side of the equation. -1a + -6i + 6i = -7 + -3bi + 6i Combine like terms: -6i + 6i = 0 -1a + 0 = -7 + -3bi + 6i -1a = -7 + -3bi + 6i Divide each side by '-1'. a = 7 + 3bi + -6i Simplifying a = 7 + 3bi + -6i
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