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If (1+i)(1+2i)(1+3i)1+m)=(x+i y) , then ...

If `(1+i)(1+2i)(1+3i)1+m)=(x+i y)` , then show that `2xx5xx10xxxx(1+n^2)=x^2+y^2dot`

Text Solution

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We have ,
`(1+i) (1+2i)(1+3i).....(1+ni) = x+iy`
`rArr |(1+i) (1+2i)...(1+ni)|=|x = iy|`
`rArr |1+ i||1+2i|....|1+ni|=|x+iy|" "[because |z_(1)z_(2)...z_(n)|=|Z_(1)||z_(2)| .....|z_(n)|]`
`rArr sqrt(1+1)sqrt(1+4).....sqrt(1+n^(2)) = sqrt(x^(2)+y^(2))`
`rArr 2xx5xx10...(1+n^(2))= (x^(2) + y^(2))`[On squaring both side]
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