Home
Class 12
MATHS
Let z be a complex number having the arg...

Let `z` be a complex number having the argument `theta` ,`0` <` theta` < `pi/2`, and satisfying the equation` |z-3i|=3.` Then find the value of `cottheta-6/z`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

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

    VMC MODULES ENGLISH|Exercise JEE ARCHIVE|76 Videos
  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise LEVEL - 1|90 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 z is a complex number of unit modulus and argument theta , then the real part of (z(1-barz))/(barz(1+z)) , is

Let z be a complex number such that the imaginary part of z is nonzero and a = z^2 + z + 1 is real. Then a cannot take the value

Let z be a complex number such that the imaginary part of z is nonzero and a = z^2 + z + 1 is real. Then a cannot take the value

Let Z be a complex number satisfying the relation Z^(3)+(4(barZ)^(2))/(|Z|)=0 . If the least possible argument of Z is -kpi , then k is equal to (here, argZ in (-pi, pi] )

The complex number having least positive argument and satisying |z-5i| le 3 , is

Let 'z' be a complex number and 'a' be a real parameter such that z^2+az+a^2=0 , then

Let z_1=10+6i and z_2=4+6idot If z is any complex number such that the argument of ((z-z_1))/((z-z_2)) is pi/4, then prove that |z-7-9i|=3sqrt(2) .

Let z be a complex number satisfying 1/2 le |z| le 4 , then sum of greatest and least values of |z+1/z| is :

bb"Statement-1" If the principal argument of a complex numbere z is 0, the principal argument of z^(2) " is " 2theta . bb"Statement-2" arg(z^(2))=2arg(z)

Let z be a complex number satisfying |z-5i|<=1 such that amp(z) is minimum, then z is equal to

VMC MODULES ENGLISH-COMPLEX NUMBERS -LEVEL - 2
  1. If cosA+cosB+cosC=0,sinA+sinB+sinC=0andA+B+C=180^(@) then the value of...

    Text Solution

    |

  2. Let |(barZ(1) - 2barz(2))//(2-z(1)barz(2))|= 1 and |z(2)| ne 1, where...

    Text Solution

    |

  3. Let z be a complex number having the argument theta ,0 < theta < pi/2,...

    Text Solution

    |

  4. If |z+2-i|=5 and maxium value of |3z +9-7i| is M, then the value of M ...

    Text Solution

    |

  5. If a, b are complex numbers and one of the roots of the equation x^(2)...

    Text Solution

    |

  6. Solve for z : z^2-(3-2i)z=(5i-5)dot

    Text Solution

    |

  7. Find number of values of complex numbers omega satisfying the system o...

    Text Solution

    |

  8. For |z-1|=1, show that tan{[a r g(z-1)]//2}-(2i//z)=-idot

    Text Solution

    |

  9. If nge3and1,alpha(1),alpha(2),.......,alpha(n-1) are nth roots of unit...

    Text Solution

    |

  10. Let |z|=2and w=(z+1)/(z-1),where z ,w , in C (where C is the set of c...

    Text Solution

    |

  11. If z=x+i y is a complex number with x ,y in Qa n d|z|=1, then show th...

    Text Solution

    |

  12. If z^3+(3+2i)z+(-1+i a)=0 has one real roots, then the value of a lies...

    Text Solution

    |

  13. Given z=f(x)+ig(x) where f,g:(0,1) to (0,1) are real valued functions....

    Text Solution

    |

  14. Let z1a n dz2 be complex numbers such that z1!=z2 and |z1|=|z2|dot If ...

    Text Solution

    |

  15. If m and x are two real number s and i=sqrt(-1), prove that e^(2mico...

    Text Solution

    |

  16. Find the range of real number alpha for which the equation z + al...

    Text Solution

    |

  17. The condition that x^(n+1)-x^(n)+1 shall be divisible by x^(2)-x+1 is ...

    Text Solution

    |

  18. Find the point of intersection of the curves a r g(z-3i)=(3pi)/4a n d ...

    Text Solution

    |

  19. If the equation z^4+a1z^3+a2z^2+a3z+a4=0 where a1,a2,a3,a4 are real co...

    Text Solution

    |

  20. The value of the expression 2(1+(1)/(omega))(1+(1)/(omega^(2)))+3(2+(1...

    Text Solution

    |