If (1+i)(1+2i)(1+3i).....(1+ni)=a+ib, then 2×5×10×....×(1+n2) is equal to

Given (1+i)(1+2i)(1+3i)....(1+ni) =a+ib             (Taking modules on the two sides)⇒   |(1+i)(1+2i)(1+3i)...(1+ni)| = |a+ib|   ⇒    12+1212+22. 12+32...12+n2 =  a2+b2Squaring on both sides⇒ 2×5×10×  ...×  (1+n2)=a2+b2