Unformatted text preview: x = a/b . A.5. Prove that for every positive integer n > 1 we have n X k =1 cos 2 πk n = 0 . Hint: Consider the number ω = cos(2 π/n ) + i sin(2 π/n ). A.6. Deﬁne a function f : C → M 2 × 2 ( R ) from the complex numbers to the 2 × 2 real matrices by setting f ( a + ib ) = ± ab b a ² . For any complex numbers z,w ∈ C verify the following: (a) f ( z + w ) = f ( z ) + f ( w ), (b) f ( zw ) = f ( z ) f ( w ), (c)  z  2 = det f ( z ). (The operations on the right hand sides of the equations are matrix addition, matrix multiplication, and matrix determinant.)...
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 Spring '11
 Armstrong
 Math, Algebra, Cos, Complex number, 1 2k, Drew Armstrong

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