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Simplifying (8 + 6i) + (44 + -17i) + -1(a + bi) = 0 Remove parenthesis around (8 + 6i) 8 + 6i + (44 + -17i) + -1(a + bi) = 0 Remove parenthesis around (44 + -17i) 8 + 6i + 44 + -17i + -1(a + bi) = 0 8 + 6i + 44 + -17i + (a * -1 + bi * -1) = 0 8 + 6i + 44 + -17i + (-1a + -1bi) = 0 Reorder the terms: 8 + 44 + -1a + -1bi + 6i + -17i = 0 Combine like terms: 8 + 44 = 52 52 + -1a + -1bi + 6i + -17i = 0 Combine like terms: 6i + -17i = -11i 52 + -1a + -1bi + -11i = 0 Solving 52 + -1a + -1bi + -11i = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-52' to each side of the equation. 52 + -1a + -1bi + -52 + -11i = 0 + -52 Reorder the terms: 52 + -52 + -1a + -1bi + -11i = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -1a + -1bi + -11i = 0 + -52 -1a + -1bi + -11i = 0 + -52 Combine like terms: 0 + -52 = -52 -1a + -1bi + -11i = -52 Add 'bi' to each side of the equation. -1a + -1bi + bi + -11i = -52 + bi Combine like terms: -1bi + bi = 0 -1a + 0 + -11i = -52 + bi -1a + -11i = -52 + bi Add '11i' to each side of the equation. -1a + -11i + 11i = -52 + bi + 11i Combine like terms: -11i + 11i = 0 -1a + 0 = -52 + bi + 11i -1a = -52 + bi + 11i Divide each side by '-1'. a = 52 + -1bi + -11i Simplifying a = 52 + -1bi + -11i
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