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

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