Home
Class 12
MATHS
Let z(1) be a fixed point on the circle...

Let `z_(1)` be a fixed point on the circle of radius 1 centered at the origin in the Argand plane and `z_(1) ne pm1`. Consider an equilateral triangle incribed in the circle with `z_(1), z_(2), z_(3)` as the vertices taken in the counter clockwise direction. Then `z_(1)z_(2)z_(3)` is equal to

A

`z_(1)^(2)`

B

`z_(1)^(3)`

C

`z_(1)^(4)`

D

`z_(1)`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2013

    WB JEE PREVIOUS YEAR PAPER|Exercise MULTIPLE CHOICE QUESTIONS|80 Videos

  • QUESTION PAPER 2015

    WB JEE PREVIOUS YEAR PAPER|Exercise MULTIPLE CHOICE QUESTIONS|80 Videos

Similar Questions

Explore conceptually related problems

Let z_(1) be a fixed point on the circle of radius 1 centered at the origin in the Argand plane and z_(1)ne+-1 . Consider an equilateral traingle inscribed in the circle with z_(1),z_(2),z_(3) as the vertices taken in the counter clockwise direction .Then z_(1)z_(2)z_(3) is equal to -

Let z_1 be a fixed point on the circle of radius 1 centered at the origin in the Argand plane and z_1 ne+-1 consider an equilateral triangle inscribed in the circle with z_1,z_2,z_3 as the vertices taken in the counter clockwise directtion then z_1z_2z_3 is equal to

if z_1, z_2, z_3 are the vertices pf an equilateral triangle inscribed in the circle absz=1 and z_1=i , then

If A(z_1), B(z_2), C(z_3) are the vertices of an equilateral triangle ABC, then arg((z_2+z_3-2z_1)/(z_3-z_2)) is equal to

If z_0 is the circumcenter of an equilateral triangle with vertices z_1, z_2, z_3 then z_1^2+z_2^2+z_3^2 is equal to

Let z_(1) and z_(2) be the roots of z ^(2)+az+b=0 . If the origin, z_(1) and z_(2) form an equilateral triangle. Then-

An equilateral triangle in the Argan plane has vertix as z_1 , z_2 and z_3 which are there complex no show that 1/(z_1-z_2)+1/(z_3-z_1)+1/(z_2-z_3)=0

If the complex numbers z_(1),z_(2),z_(3) represents the vertices of an equilaterla triangle such that |z_(1)|=|z_(2)|=|z_(3)| , show that z_(1)+z_(2)+z_(3)=0

If the points A(z),B(-z),C(1-z) are the vertices of an equilateral triangle ABC then Re(z) is

If z_1,z_2,z_3 are any three roots of the equation z^6=(z+1)^6, then arg((z_1-z_3)/(z_2-z_3)) can be equal to

WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2014-MULTIPLE CHOICE QUESTIONS
  1. Let [x] denote the greatest integer less than or equal to x for any re...

    Text Solution

    |

  2. Suppose that f(x) is a differentiable function such that f'(x) is con...

    Text Solution

    |

  3. Let z(1) be a fixed point on the circle of radius 1 centered at the o...

    Text Solution

    |

  4. Suppose that z(1), z(2), z(3) are three vertices of an equilateral tr...

    Text Solution

    |

  5. The curve y=(cosx+y)^(1//2) satisfies the differential equation

    Text Solution

    |

  6. In the Argand plane, the distinct roots of 1+z+z^(3)+z^(4)=0(z is a co...

    Text Solution

    |

  7. If A, B, C are the angles of a triangle then tan ((B+C)/2)=

    Text Solution

    |

  8. Let alpha, beta be the roots of x^(2)-x-1=0 and S(n)=a^(n)+beta^(n), f...

    Text Solution

    |

  9. A fair six-faced die is rolled 12 times. The probability that each fac...

    Text Solution

    |

  10. If alpha, beta are the roots of the quadratic equation x^(2)+px+q=0, t...

    Text Solution

    |

  11. The solution of the differential equation (dy)/(dx)+(y)/(x log(e )x)...

    Text Solution

    |

  12. Let f(x) = max {x+|x|, x-[x]}, where [x] denotes the greatest integer ...

    Text Solution

    |

  13. Let X(n)={z=x+iy:|z|^(2) le (1)/(n)} for all integers n ge 1. Then cap...

    Text Solution

    |

  14. Applying Lagrange's Mean Value Theorem for a suitable function f(x) is...

    Text Solution

    |

  15. The equation of hyperbola whose coordinates of the foci are (pm8,0) a...

    Text Solution

    |

  16. A student answers a multiple choice question with 5 alternatives, of ...

    Text Solution

    |

  17. "cos"(2pi)/(7) +"cos"(4pi)/(7)+"cos"(6pi)/(7)

    Text Solution

    |

  18. Suppose M= int(0)^(pi//2) (cos x)/(x+2) dx, N=int(0)^(pi//4) (sinx" "c...

    Text Solution

    |

  19. For any two real numbers theta and varphi, we define thetaR varphi if ...

    Text Solution

    |

  20. The minimum value of 2^(sinx)+2^(cosx) is

    Text Solution

    |