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If (2+iota)(2+2iota)(2+3iota).....(2+9io...

If `(2+iota)(2+2iota)(2+3iota).....(2+9iota)=x+iotay`, then 5.8.13.....85=

Text Solution

Verified by Experts

`|z|=|x+iy|=sqrt(x^2+y^2)`
`|x+iy|=|(2+i)(2+2i)(2+3i)...(2+9i)|`
`=|2+i||2+2i||2+3i|...|2+9i|`
`=sqrt(4+1)*sqrt(2^2+2^2)...sqrt(2^2+9^2)`
`sqrt(x^2+y^2)=sqrt5*sqrt8*sqrt13...sqrt85`
`x^2+y^2=5*8*13*...*85`
option 1 is correct.
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