1.

Let z_k=cos((2kpi)/(10))+isin ((2kpi)/10),k=1,2,......9 {:("List I","List II"),((P) " For each " z_k"there exists a " z_j" such that " z_k.z_j=1,1."True"),((Q)"There exists a "k in{1,2,....9}"such that "z_1.z=z_k" has no solution z in the set of complex numbers.",2. False),((R)(|1-z_1||1-z_2|....|1-z_9|)/10 "equal ",3.1),((S)1-sum_(k=1)^9cos((2kpi)/(10))"equal" ,4.2):}

Answer»

<P>`{:(P,Q,R,S),(1,2,4,3):}`
`{:(P,Q,R,S),(2,1,3,4):}`
`{:(P,Q,R,S),(1,2,3,4):}`
`{:(P,Q,R,S),(2,1,4,3):}`

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