M135F08AXS

M135F08AXS - MATH 135 Fall 2008 Assignment X Solutions...

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Unformatted text preview: MATH 135 Fall 2008 Assignment X Solutions Hand-In Problems None Recommended Problems 1. 1 + i 5 = 1- i 5 and | 1 + i 5 | = q 1 2 + ( 5) 2 = 6 2.- i = 0 + i (- 1) = 0- i (- 1) = i and | - i | = | 0 + i (- 1) | = p 2 + (- 1) 2 = 1 = 1 3. 2 = 2 + 0 i = 2- i = 2 and | 2 | = | 2 + 0 i | = 2 2 + 0 2 = 4 = 2 4. If z = 1 + i , then z 2 = (1 + i )(1 + i ) = 2 i z 3 = z 2 z = (2 i )(1 + i ) =- 2 + 2 i z 4 = z 2 z 2 = (2 i )(2 i ) =- 4 1 z = 1 1 + i = 1- i (1 + i )(1- i ) = 1- i 2 = 1 2- 1 2 i . which gives 6 ?- t z t z 2 @ @ @ @ @ @ t z 3 @ @ t 1 /z t z 4 5. If z has polar coordinates ( 3 , 3 / 4), then z = 3 cis ( 3 4 ) = 3 ( cos ( 3 4 ) + i sin ( 3 4 )) = 3- 1 2 + 1 2 i =- 3 2 + 3 2 i =- 6 2 + 6 2 i 6. If z has polar coordinates (7 , 7 / 6), then z = 7 cis ( 7 6 ) = 7 ( cos ( 7 6 ) + i sin ( 7 6 )) = 7- 3 2- 1 2 i =- 7 3 2- 7 2 i 7. If z has polar coordinates (1 ,- 2 / 3), then z = 1 cis (- 2 3 ) = cos (- 2 3 ) + i sin (- 2 3 ) =- 1 2- 3 2 i 8. Let z =- 6 + 3 2 i Then | z | = q (- 6) 2 + (3...
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M135F08AXS - MATH 135 Fall 2008 Assignment X Solutions...

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