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Simplifying (6 + 3i) + (14 + -7i) + -1(a + bi) = 0 Remove parenthesis around (6 + 3i) 6 + 3i + (14 + -7i) + -1(a + bi) = 0 Remove parenthesis around (14 + -7i) 6 + 3i + 14 + -7i + -1(a + bi) = 0 6 + 3i + 14 + -7i + (a * -1 + bi * -1) = 0 6 + 3i + 14 + -7i + (-1a + -1bi) = 0 Reorder the terms: 6 + 14 + -1a + -1bi + 3i + -7i = 0 Combine like terms: 6 + 14 = 20 20 + -1a + -1bi + 3i + -7i = 0 Combine like terms: 3i + -7i = -4i 20 + -1a + -1bi + -4i = 0 Solving 20 + -1a + -1bi + -4i = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -1a + -1bi + -20 + -4i = 0 + -20 Reorder the terms: 20 + -20 + -1a + -1bi + -4i = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1a + -1bi + -4i = 0 + -20 -1a + -1bi + -4i = 0 + -20 Combine like terms: 0 + -20 = -20 -1a + -1bi + -4i = -20 Add 'bi' to each side of the equation. -1a + -1bi + bi + -4i = -20 + bi Combine like terms: -1bi + bi = 0 -1a + 0 + -4i = -20 + bi -1a + -4i = -20 + bi Add '4i' to each side of the equation. -1a + -4i + 4i = -20 + bi + 4i Combine like terms: -4i + 4i = 0 -1a + 0 = -20 + bi + 4i -1a = -20 + bi + 4i Divide each side by '-1'. a = 20 + -1bi + -4i Simplifying a = 20 + -1bi + -4i
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