यदि `(a_(1) + ib_(1)) (a_(2) + ib_(2)) = A + "iB"` हो, तो `"tan"^(-1)((b_(1))/(a_(1))) + "tan"^(-1)((b_(2))/(a_(2)))` हो, तो

Given that (a_(1)+ib_(1))(a_(2)+ib_(2)) . . . .(a_(n)+ib_(n))=c+id , show that: tan^(-1)((b_(1))/(a_(1)))+tan^(-1)((b_(2))/(a_(2)))+ . . .+tan^(-1)((b_(n))/(a_(n)))=mpi+tan^(-1)((d)/(c)) .

Given that: (a_(1)+ib_(1))(a_(2)+ib_(2)) . . . (a_(n)+ib_(n))=c+id , show that: tan^(-1)((b_(1))/(a_(1)))+tan^(-1)((b_(2))/(a_(2)))+ . . .+tan^(-1)((b_(n))/(a_(n))) =mpi+tan^(-1)((d)/(c)) .

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

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 0

If a_(1), a_(2), a_(3),...., a_(n) is an A.P. with common difference d, then prove that tan[tan^(-1) ((d)/(1 + a_(1) a_(2))) + tan^(-1) ((d)/(1 + a_(2) a_(3))) + ...+ tan^(-1) ((d)/(1 + a_( - 1)a_(n)))] = ((n -1)d)/(1 + a_(1) a_(n))