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quiz 6A sol - Solutions to Quiz 6A www.math.u.edu/harringt...

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Solutions to Quiz 6A www.math.ufl.edu/˜harringt October 5, 2007 1. Reduce and simplify (a) (3+2 i ) 5 7 i (1 + i 2 ) = (3+2 i ) 5 7 i (1 - 1) = (3+2 i ) 5 7 i * 0 = 0 (b) i 21 = ( i 4 ) 5 * i = (1) 5 * i = i 2. Solve for x : (a) 3 + 2 | x + 4 | = 0 2 | x + 4 | = - 3 | x + 4 | = - 3 2 Since | x | ≥ 0 for all x R then | x + 4 | = - 3 2 has no solution. So the solution set is . (b) 3 + 3 x + 1 = x (1) 3 x + 1 = x - 3 (2) ( 3 x + 1) 2 = ( x - 3) 2 (3) 3 x + 1 = x 2 - 6 x + 9 (4) 0 = x 2 - 9 x + 8 (5) 0 = ( x - 8)( x - 1) (6) So x = 8 and x = 1. However in step (3) we could have created extranenous solutions. Thus, we must check our solutions. 1
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Check x = 8: 3 + 3 * 8 + 1 = 3 + 25 = 8. So 8 works. Check x = 1: 3 +
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