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test5-fall94

# 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 θ be a real number. (i) Let n > 1 be an integer. SHOW using DeMoivre’s theorem that ( e iθ ) n = e iθn . (ii) PROVE cos θ = 1 2 ( e iθ + e-iθ ) sin θ = 1 2 i ( e iθ-e-iθ ) (iii) (a) EXPAND ( e iθ + e-iθ ) 3 and SIMPLIFY. (b) Hence SHOW that cos3 θ = 4 cos 3 θ-3 cos θ. 1...
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