If \( (1+i)(1+2 i)(1+3 i) \ldots . .(1+n i)=a+i b \), then \( 2.5 .10 .17 \ldots \ldots\left(1+n...

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If \( (1+i)(1+2 i)(1+3 i) \ldots . .(1+n i)=a+i b \), then \( 2.5 .10 .17 \ldots \ldots\left(1+n^{2}\right)= \)
(A) \( a-i b \)
(B) \( a^{2}-b^{2} \)
(C) \( a^{2}+b^{2} \)
(D) none of these
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