test5-fall94 - rectangular form and simplify . EXHIBIT your...

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Name: S.S.N: MAS 3300 – Test 5 Fall 1994 In giving proofs make sure your reasoning is clear. The questions have equal value. You may use your unmarked printed course notes. Calculators are allowed. Write on ONE side of your paper. 1. FIND the sum, product and quotient of 2 - 3 i and 1 + i . 2. Let z = - 3 - i . WRITE z in polar form. 3. PROVE If z 1 , z 2 C then z 1 z 2 = z 1 z 2 . 4. PROVE that C satisfies the MIV axiom. 5. FIND all solutions in C to w 4 + 81 = 0 . WRITE your solutions in
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Unformatted text preview: rectangular form and simplify . EXHIBIT your solutions geometrically. 6. Let be a real number. (i) Let n > 1 be an integer. SHOW using DeMoivres theorem that ( e i ) n = e in . (ii) PROVE cos = 1 2 ( e i + e-i ) sin = 1 2 i ( e i-e-i ) (iii) (a) EXPAND ( e i + e-i ) 3 and SIMPLIFY. (b) Hence SHOW that cos3 = 4 cos 3 -3 cos . 1...
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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.

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