Home
Class 11
MATHS
In the Argand plane the distinct roots o...

In the Argand plane the distinct roots of `1+z+z^3+z^4=0` (z is a complex number) represent vertices of

A

a square

B

an equilateral triangle

C

a rhombus

D

a rectangle

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    PATHFINDER|Exercise QUESTION BANK|198 Videos

  • COMPLEX NUMBERS

    PATHFINDER|Exercise QUESTION BANK|67 Videos

Similar Questions

Explore conceptually related problems

Given that the complex numbers which satisfy the equation | z bar z ^3|+| bar z z^3|=350 form a rectangle in the Argand plane with the length of its diagonal having an integral number of units, then area of rectangle is 48 sq. units if z_1, z_2, z_3, z_4 are vertices of rectangle, then z_1+z_2+z_3+z_4=0 rectangle is symmetrical about the real axis a r g(z_1-z_3)=pi/4or(3pi)/4

If |z+i|-|z-1|=|z|-2=0 for a complex number z, then z =

Suppose that z_1, z_2, z_3 are three vertices of an equilateral triangle in the Argand plane let alpha=1/2(sqrt3+i) and beta be a non zero complex number the point alphaz_1+beta,alphaz_2+beta,alphaz_3+beta wil be

If z^4+1=sqrt(3)i (A) z^3 is purely real (B) z represents the vertices of a square of side 2^(1/4) (C) z^9 is purely imaginary (D) z represents the vertices of a square of side 2^(3/4)

If in argand plane the vertices A,B,C of an isoceles triangle are represented by the complex nos z_1 ,z_2, z_3 respectively where angleC=90^@ then show that (z_1-z_2)^2=2(z_1-z_3)(z_3-z_2)

Number of solutions of the equation z^3+[3(barz)^2]/|z|=0 where z is a complex number is

Let z be a complex number satisfying |z+16|=4|z+1| . Then

Consider the region R in the Argand plane described by the complex number. Z satisfying the inequalities |Z-2| le |Z-4| , |Z-3| le |Z+3| , |Z-i| le |Z-3i| , |Z+i| le |Z+3i| Answer the followin questions : Minimum of |Z_(1)-Z_(2)| given that Z_(1) , Z_(2) are any two complex numbers lying in the region R is

If one root of the equation z^2-a z+a-1= 0 is (1+i), where a is a complex number then find the root.

Consider the region R in the Argand plane described by the complex number. Z satisfying the inequalities |Z-2| le |Z-4| , |Z-3| le |Z+3| , |Z-i| le |Z-3i| , |Z+i| le |Z+3i| Answer the followin questions : The maximum value of |Z| for any Z in R is

PATHFINDER-COMPLEX NUMBER-QUESTION BANK
  1. If z is a complex number such that abszge2 then the minimum value of a...

    Text Solution

    |

  2. Let z1,z2 be two fixed complex numbers in the Argand plane and z be an...

    Text Solution

    |

  3. In the Argand plane the distinct roots of 1+z+z^3+z^4=0 (z is a comple...

    Text Solution

    |

  4. Suppose that z1, z2, z3 are three vertices of an equilateral triangle ...

    Text Solution

    |

  5. The value of absz^2+abs(z-3)^2+abs(z-i)^2 is minimum when z equals

    Text Solution

    |

  6. Let z1 be a fixed point on the circle of radius 1 centered at the orig...

    Text Solution

    |

  7. Let alpha ,beta denote the cube roots of unity other than 1 and alpha ...

    Text Solution

    |

  8. Let complex numbers alpha and 1/alpha^- lie on circles (x-x0)^2+(y-y0...

    Text Solution

    |

  9. If z is a complex number of unit modulus and argument theta then arg(...

    Text Solution

    |

  10. Let z1=2+3i and z2=3+4i be two points on the complex plane then the se...

    Text Solution

    |

  11. Suppose z=x+iy where x and y are real numbers and i=sqrt(-1) the point...

    Text Solution

    |

  12. If P,Q,R are angles of an isosceles triangle and anglep=pi/2 then the ...

    Text Solution

    |

  13. Let z be a complex number such that the imaginary part of z is non zer...

    Text Solution

    |

  14. If z ne 1 and (z^2)/(z-1) is real then the point represented by the co...

    Text Solution

    |

  15. The maximum value of absz when the complex number z satisfies the cond...

    Text Solution

    |

  16. If (3/2+isqrt3/2)^50=3^25(x+iy)where x and y are real then the order P...

    Text Solution

    |

  17. If (z-1)/(z+1) is purely imaginary then

    Text Solution

    |

  18. The points representing the complex number z for which arg((z-2)/(z+2)...

    Text Solution

    |

  19. if z is any complex number satisfying abs(z-3-2i)le2 then the minimum ...

    Text Solution

    |

  20. Let omega=e^(ipi/3),and a,b,c,x,y,z be non zero complex numbers such t...

    Text Solution

    |