Home
Class 11
MATHS
Given that: (a(1)+ib(1))(a(2)+ib(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))`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise COMPETITION FILE|17 Videos

  • COMPLEX NUMBERS

    MODERN PUBLICATION|Exercise EXERCISE|10 Videos

  • BINOMIAL THEOREM

    MODERN PUBLICATION|Exercise COMPETITION FILE (JEE MAIN)|11 Videos

  • CONIC SECTIONS

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|12 Videos

Similar Questions

Explore conceptually related problems

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 (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 .

If 0

If (1+x)^(n) = a_(0) + a_(1)x + a_(2)x^(2) + ....+a_(n)x^(n) , then (1+(a_(1))/(a_(0)))(1+(a_(2))/(a_(1)))(1+(a_(3))/(a_(2)))...(1+(a_(n))/(a_(n-1)))=

If a_(1),a_(2),a_(3),….a_(n) is a.p with common difference d then tan{tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a_(2)a_(3))) +..+ tan^(-1)((d)/(1+a_(n-1)a_(n)))} is equal to

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_(n-1)a_(n)))]=((n-1)d)/(1+a_(1)a_(n))