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Unformatted text preview: Prove that NO order relation can be placed on C so that C becomes an ordered eld. 7. Let r , s 0, , R . Let z 1 = r (cos + i sin ) , z 2 = s (cos + i sin ) . Prove that z 1 z 2 = rs (cos( + ) + i sin( + )) . 8. Determine all solutions z in C of the equation z 3 + 64 i = 0 . Write the solutions in rectangular form and simplify. Exhibit the solutions geomet-rically. 9. Let R . (a) Prove that cos = 1 2 ( e i + e-i ). (b) Prove that sin = 1 2 i ( e i-e-i ). (c) Expand ( e i + e-i ) 3 and simplify. (d) Hence show that cos 3 = 1 4 cos3 + 3 4 cos ....
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This note was uploaded on 06/03/2011 for the course MAS 3300 taught by Professor Staff during the Spring '08 term at University of Florida.
- Spring '08