question_answer

If \[i=\sqrt{-1}\] and\[\left( 1+\frac{1}{{{1}^{2}}} \right).\left( 1+\frac{1}{{{(1+i)}^{2}}} \right)\left( 1+\frac{1}{{{(1+2i)}^{2}}} \right)\]\[...........\left( 1+\frac{1}{{{(1+(n-1)i)}^{2}}} \right)=\frac{10+8i}{1+8i},\]then n is equal to                        

A)  7                                            

B)  8

C)  9                                            

D)  11