1.

Consider an equation z^(197)=1(z is a complex number). If alpha, beta are its two randomly chosen roots. 'p' denotes the probability that sqrt(2+sqrt(3)) le|alpha+beta|, then

Answer»

`p=1/1996,aepsilonI`
`[1/p]` lies in `[5,15]`
`[1/pxx83/50]` is 8 is divisible by 2
`[1/p]+2` is 6

Solution :Take `beta=1`
`implies|1+alpha|^(2)=|(1+costheta)+isintheta|^(2)=2+2costhetage2+SQRT(3)`
`impliescosthetage(sqrt(3))/2` so, we GET 332 angles
`:.p=332/1996`


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