If $(a_1+ib_1)(a_2+ib_2)......................(a_n+ib_n)=c+id$ then what is the value of $tan^{-1}\large\frac{b_1}{a_1}$+$tan^{-1}\large\frac{b_2}{a_2}$+............................$tan^{-1}\large\frac{b_n}{a_n}$?

Question

(A) $n\pi-tan^{-1}\large(\frac{d}{c})$ (B) $n\pi+tan^{-1}\large(\frac{d}{c})$ (C) $2n\pi-tan^{-1}\large(\frac{d}{c})$ (D) $2n\pi+tan^{-1}\large(\frac{d}{c})$