Home
Class 12
MATHS
If one of the vertices of the square cir...

If one of the vertices of the square circumscribing the circle `abs(z-1)=sqrt(2)` is `2+sqrt(3)i`, where `i=sqrt(-1)` . Find the other vertices of the square.

Text Solution

Verified by Experts

The correct Answer is:
` x_(2) = - sqrt(3)I,x_(3) = (1 - sqrt(3) + " i and " z_(4) = (1 + sqrt(3)) - I `
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    VMC MODULES ENGLISH|Exercise NUMRICAL VALUE TYPE FOR JEE MAIN|14 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 one of the vertices of the square circumscribing the circle |z - 1| = sqrt2 is 2+ sqrt3 iota . Find the other vertices of square

Let one of the vertices of the square circumseribing the circle x^(2) + y^(2) - 6x -4y + 11 = 0 be (4, 2 + sqrt(3)) The other vertices of the square may be

If z=ilog_(e)(2-sqrt(3)),"where"i=sqrt(-1) then the cos z is equal to

If a=(1+i)/sqrt2," where "i=sqrt(-1), then find the value of a^(1929) .

If one side of the square is 2x-y+6=0, then one of the vertices is (2,1) . Find the other sides of the square.

If one side of the square is 2x-y+6=0, then one of the vertices is (2,1) . Find the other sides of the square.

If |z-2-3i|+|z+2-6i|=4 where i=sqrt(-1) then find the locus of P(z)

If |z-2i|lesqrt(2), where i=sqrt(-1), then the maximum value of |3-i(z-1)|, is

The center of a square is at the origin and its one vertex is A(2,1) . Find the coordinates of the other vertices of the square.

The center of a square is at the origin and its one vertex is A(2,1)dot Find the coordinates of the other vertices of the square.

VMC MODULES ENGLISH-COMPLEX NUMBERS -JEE ARCHIVE
  1. about to only mathematics

    Text Solution

    |

  2. Find the centre and radius of the circle formed by all the points repr...

    Text Solution

    |

  3. If one of the vertices of the square circumscribing the circle abs(z-1...

    Text Solution

    |

  4. Let a complex number alpha,alpha!=1, be a rootof hte euation z^(p+q)-z...

    Text Solution

    |

  5. If x+i y=sqrt((a+i b)/(c+i d)) prove that (x^2+y^2)^2=(a^2+b^2)/(c^2+d...

    Text Solution

    |

  6. If x=a+b,y=a alpha+b beta and z=abeta+ b alpha , where alpha and beta...

    Text Solution

    |

  7. Express 1//(1-costheta+2isintheta) in the form x=i y .

    Text Solution

    |

  8. If n is n odd integer that is greater than or equal to 3 but not a mul...

    Text Solution

    |

  9. The real values of xa n dy for which the following equation is satisfi...

    Text Solution

    |

  10. Let the complex numbers z(1),z(2) and z(3) be the vertices of an equ...

    Text Solution

    |

  11. A relation R on set of complex numbers defined by Z(1)RZ(2) hArr (Z(1)...

    Text Solution

    |

  12. Prove that the complex numbers z(1),z(2) and the origin form an equ...

    Text Solution

    |

  13. If roots of an equation x^n-1=0a r e1,a1,2, a(n-1), then the value of...

    Text Solution

    |

  14. Show that the area of the triangle on the Argand diagram formed by the...

    Text Solution

    |

  15. Complex numbers z(1),z(2)andz(3) are the vertices A,B,C respectivelt o...

    Text Solution

    |

  16. If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2...

    Text Solution

    |

  17. If |z|<=1,|w|<=1, then show that |z- w|^2<=(|z|-|w|)^2+(argz-argw)^2

    Text Solution

    |

  18. Find the non-zero complex number z satisfying z =i z^2dot

    Text Solution

    |

  19. Let z1 \and\ z2 be the roots of the equation z^2+p z+q=0, where the co...

    Text Solution

    |

  20. Let barz+bbarz=c,b!=0 be a line the complex plane, where bar b is the ...

    Text Solution

    |