Home
Class 12
MATHS
If (a1+ib1)(a2+ib2).....(an+ibn)=A+iB, t...

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)`

A

1

B

`A^(2)+B^(2)`

C

`A+B`

D

`1/A^(2)+1/B^(2)`

Text Solution

Verified by Experts

The correct Answer is:
b
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|58 Videos
  • COMPLEX NUMBERS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|15 Videos
  • CIRCLES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|53 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|87 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, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

If a_1,a_2 ...a_n are nth roots of unity then 1/(1-a_1) +1/(1-a_2)+1/(1-a_3)..+1/(1-a_n) is equal to

cIf a_1,a_2,a_3,..,a_n in R then (x-a_1)^2+(x-a_2)^2+....+(x-a_n)^2 assumes its least value at x=

If (1+x)^n=a_0+a_1x+a_2x^2+....+a_nx^n , then (a_0-a_2+.....)^2+(a_1-a_3+.....)^2 is equal to (A) 3^n (B) 2^n (C) ((1-2^n)/(1+2^n)) (D) none of these

If f(x)=(a_1x+b_1)^2+(a_2x+b_2)^2+...+(a_n x+b_n)^2 , then prove that (a_1b_1+a_2b_2+...+a_n b_n)^2lt=(a_1^ 2+a_2^ 2+...+a_ n^2)(b_1^ 2+b_2^ 2+..+b_ n^2)dot

If A=[(n,0 ,0),( 0,n,0),( 0, 0,n)] and B=[(a_1,a_2,a_3),(b_1,b_2,b_3),(c_1,c_2,c_3)] , then A B is equal to (A) B (B) n B (C) B^n (D) A+B

If a_1,a_2,a_3….a_(2n+1) are in A.P then (a_(2n+1)-a_1)/(a_(2n+1)+a_1)+(a_2n-a_2)/(a_(2n)+a_2)+....+(a_(n+2)-a_n)/(a_(n+2)+a_n) is equal to

If S=a_1+a_2+......+a_n,a_i in R^+ for i=1 to n, then prove that S/(S-a_1)+S/(S-a_2)+......+S/(S-a_n) ge n^2/(n-1), AA n ge 2

If a_1, a_2,...... ,a_n >0, then prove that (a_1)/(a_2)+(a_2)/(a_3)+(a_3)/(a_4)+.....+(a_(n-1))/(a_n)+(a_n)/(a_1)> n

OBJECTIVE RD SHARMA ENGLISH-COMPLEX NUMBERS -Exercise
  1. If g(x) and h(x) are two polynomials such that the polynomials P(x)=g(...

    Text Solution

    |

  2. if x(k) = cos pi/3^(k) + isin pi/3^(k) , find x(1)x(2)x(3)……oo (...

    Text Solution

    |

  3. If (a1+ib1)(a2+ib2).....(an+ibn)=A+iB, then (a1^2+b1^2)(a2^2+b2^2).......

    Text Solution

    |

  4. If (a(1)+ib(1))(a(2)+ib(2))………………(a(n)+ib(n))=A+iB, then sum(i=1)^(n) ...

    Text Solution

    |

  5. If cosalpha+2cosbeta+3cosgamma=sinalpha+2sinbeta+3singamma=0,t h e nt ...

    Text Solution

    |

  6. If alpha,betaandgamma are the cube roots of P(p)lt0), then for any x, ...

    Text Solution

    |

  7. prove that tan(i" In"((a-ib)/(a+ib)))=(2ab)/(a^(2)-b^(2)) (where a, ...

    Text Solution

    |

  8. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

    Text Solution

    |

  9. The locus of the points representing the complex numbers z for which |...

    Text Solution

    |

  10. For n=6k, k in z, ((1-isqrt(3))/(2))^(n)+((-1-isqrt(3))/(2))^(n) has t...

    Text Solution

    |

  11. The product of all values of (cosalpha+isinalpha)^(3//5) is

    Text Solution

    |

  12. If C^(2)+S^(2)=1, then (1+C+iS)/(1+C-iS) is equal to

    Text Solution

    |

  13. The centre of a square ABCD is at z=0, A is z(1). Then, the centroid o...

    Text Solution

    |

  14. The number of solutions of the system of equations "Re(z^(2))=0, |z|=2...

    Text Solution

    |

  15. The vector z=-4+5i is turned counter clockwise through an angle of 180...

    Text Solution

    |

  16. The value of [sqrt(2)(cos(56^(@)15^('))+isin(56^(@)15^('))]^(8), is

    Text Solution

    |

  17. Find the complex number z satisfying the equation |(z-12)/(z-8i)|= (5)...

    Text Solution

    |

  18. The vertices B and D of a parallelogram are 1-2i and 4-2i If the diago...

    Text Solution

    |

  19. If the complex number z(1) " and " z(2) are such that arg (z(1)) - ar...

    Text Solution

    |

  20. The join of z(1)=a+ib and z(2)=1/(-a+ib) passes through

    Text Solution

    |