If `(a_1+ib_1)(a_2+ib_2).....(a_n+ib_n)=A+iB`, then `(a_1^2+b_1^2)(a_2^2+b_2^2)......(a_n^2+b_n^2)` is equal to (A) 1 (B) `(A^2+B^2)` (C) `(A+B)` (D) `(1/A^2+1/B^2)`

If (a_1+ib_1)(a_2+ib_2)...(a_n+ib_n) = x+iy , prove that : (a_1^2+b_1^2)(a_2^2+b_2^2)...(a_n^2+b_n^2)=x^2+y^2 .

If quad (a_(1)+ib_(1))(a_(2)+ib_(2))....(a_(n)+ib_(n))=A+iB, then (a_(1)^(2)+b_(1)^(2))(a_(2)^(2)+b_(2)^(2))......(a_(n)^(2)+b_(n)^(2)) is equal to (A)1(B)(A^(2)+B^(2))(C)(A+B)(D)((1)/(A^(2))+(1)/(B^(2)))

If (a_(1)+ib_(1))(a_(2)+ib_(2))………………(a_(n)+ib_(n))=A+iB , then sum_(i=1)^(n) tan^(-1)(b_(i)/a_(i)) is equal to

Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these

Let the sequence a_1 , a_2 , a_3 ......... a_n form an A.P. then a_1^2 - a_2^2 + a_3^2 - a_4^2 +.....+ a_(2n-1)^2 - a_(2n)^2 is equal to:- (1) n/(2n-1)(a_1^2-a_(2n)^2) (2) (2n)/(n-1)(a_(2n)^2-a_1^2) (3) n/(n+1)(a_1^2+a_(2n)^2) (4)none of these

Let the sequencea_1,a_2....a_n form and AP. Then a_1^1-a_2^2+a_3^2-a_4^2... is equal to

If (a_1+ib_1)(a_2+ib_2)...(a_n+ib_n) = x+iy , prove that : tan^-1frac(b_1)(a_1)+tan^-1frac(b_2)(a_2)+...+tan^-1frac(b_n)(a_n)=tan^-1fracyx .