Given that $(1+i)(1+2i)(1+3i)\cdots(1+ni)=a+ib$, find the value of \(2\times5\times10\times\l

Question

Given that $(1+i)(1+2i)(1+3i)\cdots(1+ni)=a+ib$, find the value of $2\times5\times10\times\ldots\times(1+n^2)$ in terms of $a$ and $b$.

Accepted Answer

$a^2 + b^2$.

Modulus of a product of complex numbers