Home
Class 12
MATHS
If sqrt(3)+i=(a+i b)//(c+i d) , then fin...

If `sqrt(3)+i=(a+i b)//(c+i d)` , then find the value of `tan^(-1)(b//a)tan^(-1)(d//c)dot`

A

`2 n pi - pi/2, n in Z`

B

`2 n pi + pi/2, n in Z`

C

` n pi - pi/2, n in Z`

D

` n pi + pi/2, n in Z`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise LEVEL - 2|50 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 Videos

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos

  • CIRCLES

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ( ARCHIVE )|68 Videos

  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos

Similar Questions

Explore conceptually related problems

If (sqrt(8)+i)^(50)=3^(49)(a+i b) , then find the value of a^2+b^2dot

If x+i y=sqrt((a+i b)/(c+i d)), then write the value of (x^2+y^2)^2 .

If tan(A+B)=sqrt(3)andsin(A-B)=(1)/(2) ,then find the value of tan (2A-3B) .

If a ,\ b ,\ c >0 such that a+b+c=a b c , find the value of tan^(-1)a+tan^(-1)b+tan^(-1)c .

In a DeltaABC , if b=sqrt(3)+1, c=sqrt(3)-1 and A=60^(@) , then the value of tan.(B-C)/(2) is

Let a , b , c , d be positive integers such that (log)_a b=3/2a n d(log)_c d=5/4dot If (a-c)=9, then find the value of (b-d)dot

In a Delta ABC b= sqrt(3)+1, c=sqrt(3)-1 , angle A = 60 ^@ then the value of tan (B-C)/(2) is :-

sum_(i=1)^(2n) sin^(-1)(x_i)=npi then the value of sum_(i=1)^n cos^(-1)x_i+sum_(i=1)^n tan^(-1)x_i= (A) (npi)/4 (B) (2/3)npi (C) (5/4)npi (D) 2npi

In a triangle A B C , , if C is a right angle, then tan^(-1)(a/(b+c))+tan^(-1)(b/(c+a))= (a) pi/3 (b) pi/4 (c) (5pi)/2 (d) pi/6

If A= tan^-1((xsqrt3)/(2k-x)) and B= tan^-1((2x-k)/(ksqrt3)) then find the value of A-B (A) 0^@ (B) 30^@ (C) 60^@ (D) 45^@

VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 1
  1. If z1,z2 are two complex numbers such that Im(z1+z2)=0,Im(z1z2)=0, the...

    Text Solution

    |

  2. (1+2i+3i^2)/(1-2i+3i^2) equals i b. -i c. -1 d. 4

    Text Solution

    |

  3. If sqrt(3)+i=(a+i b)//(c+i d) , then find the value of tan^(-1)(b//a)t...

    Text Solution

    |

  4. If |z(1)|=|z(2)|andamp(z(1))+amp(z(2))=0, then

    Text Solution

    |

  5. If omega is a complex cube root of unity, then (1-omega+omega^(2))^(6...

    Text Solution

    |

  6. If omega(!= 1) be an imaginary cube root of unity and (1+omega^2)^n=(...

    Text Solution

    |

  7. Prove that x^(3p) + x^(3q+1) + x^(3r+2) is exactly divisible by x^2+x+...

    Text Solution

    |

  8. If z= x + yi and omega = ((1- zi))/(z-i), then |omega|=1 implies that ...

    Text Solution

    |

  9. The locus of z which satisfies the inequality log (0.3) abs(z-1) gt l...

    Text Solution

    |

  10. The set of points in an Argand diagram which satisfy both abs(z)le4 an...

    Text Solution

    |

  11. If the points represented by complex numbers z(1)=a+ib, z(2)=c+id " an...

    Text Solution

    |

  12. For x(1), x(2), y(1), y(2) in R if 0 lt x(1)lt x(2)lt y(1) = y(2)...

    Text Solution

    |

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

    Text Solution

    |

  14. If z(1) , z(2), z(3) are three complex numbers in A.P., then they lie ...

    Text Solution

    |

  15. If the cube roots of unity are 1,omega,omega^2, then the roots of the ...

    Text Solution

    |

  16. about to only mathematics

    Text Solution

    |

  17. If Re ((z + 2i)/(z+4))= 0 then z lies on a circle with centre :

    Text Solution

    |

  18. If z is a complex number satisfying the relation |z+ 1|=z+2(1+i), then...

    Text Solution

    |

  19. The number of solutions of z^3+ z =0 is (a) 2 (b) 3 (c) 4 (d) 5

    Text Solution

    |

  20. If z= costheta+isintheta , then the value of (z^(2n)-1)/(z^(2n)+1) ...

    Text Solution

    |