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If (a(1)+ib(1))(a(2)+ib(2))………………(a(n)+i...

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

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If (a_(1) + ib_(1)) (a_(2) + ib_(2)) … (a_(n) + ib_(n)) = A + iB then Tan^(-1) ((b_(1))/(a_(1))) + Tan^(-1) ((b_(2))/(a_(2))) + …. + Tan^(-1) ((b_(n))/(a_(n))) =

If A+iB=(a_(1)+ib_(1))(a_(2)+ib_(2))(a_(3)+ib_(3)) then A^(2)+B^(2) is :

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)) equals :

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)))

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)) .