Home
Class 11
MATHS
If z=((1+isqrt3)^2)/(4i(1-isqrt3)) is a ...

If `z=((1+isqrt3)^2)/(4i(1-isqrt3))` is a complex number then a. `arg(z)=pi/4` b. `arg(z)=pi/2` c. `|z|=1/2` d. `|z|=2`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If z=-i-1 is a complex number,then arg (z) will be

if arg(z+a)=pi/6 and arg(z-a)=(2pi)/3 then

Z is a complex number. If I Z l = 4 and arg(Z)=(5pi)/6 ,then the value of Z is

The points representing the complex number z for which arg((z-2)/(z+2))=pi/3 lie on

If z =(-2)/(1+sqrt3i), then the value of arg(z) is-

If z_1,z_2 and z_3,z_4 are two pairs of conjugate complex numbers, then arg(z_1/z_4)+arg(z_2/z_3) equals

If the argument of a complex number Z - 2 - 3i is pi/4 then the locus of z = x + iy is

Find the point of intersection of the curves a r g(z-3i)=(3pi)/4 and arg(2z+1-2i)=pi//4.

The points representing the complex number z for which arg ((z-2)/(z+2))=(pi)/(3) lie on -

The points representing the complex number z for which arg ((z-2)/(z+2))=(pi)/(3) lie on

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If alpha,beta are the roots of x^2+p x+q=0a n dx^(2n)+p^n x^n+q^n=0a n...

    Text Solution

    |

  2. If (log)(sqrt(3))((|z|^2-|z|+1)/(2+|z|))>2, then locate the region in ...

    Text Solution

    |

  3. If z=((1+isqrt3)^2)/(4i(1-isqrt3)) is a complex number then a. arg(...

    Text Solution

    |

  4. If alpha,beta,gamma are such that alpha+beta+gamma=2,""alpha^2+beta^2+...

    Text Solution

    |

  5. If z=3/(2+costheta+isintheta) then show that z lies on a circle in the...

    Text Solution

    |

  6. If z=x +i y such that |z+1|=|z-1| and arg((z-1)/(z+1))=pi/4 , then fin...

    Text Solution

    |

  7. If x y=2(x+y),xlt=y and x ,y in N , then the number of solutions of t...

    Text Solution

    |

  8. If I m((z-1)/(e^(thetai))+(e^(thetai))/(z-1))=0 , then find the locus ...

    Text Solution

    |

  9. If pa n dq are distinct prime numbers, then the number of distinct im...

    Text Solution

    |

  10. The number of real solutions of the equation (9//10)^x=-3+x-x^2 is a. ...

    Text Solution

    |

  11. What is locus of z if |z-1-sin^(-1)(1/sqrt3)|+|z+cos^(-1)(1/sqrt3)-p...

    Text Solution

    |

  12. If abs(z-2-i)=abszabssin(pi/4-argz) then locus of z is

    Text Solution

    |

  13. The number of integral values of a for which the quadratic equation (x...

    Text Solution

    |

  14. Ifomega is the imaginary cube root of unity and a+b+c=0 then show that...

    Text Solution

    |

  15. If z is a complex number having least absolute value and |z-2+2i|=1,th...

    Text Solution

    |

  16. If the equation cot^4x-2cos e c^2x+a^2=0 has at least one solution, th...

    Text Solution

    |

  17. Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/...

    Text Solution

    |

  18. If omega is the imaginary cube root of 1 then prove that (a+bomega+com...

    Text Solution

    |

  19. The number of the real solutions of the equation x^2-3absx+2=0 is

    Text Solution

    |

  20. If |z-1| + |z + 3| le 8, then prove that z lies on the circle.

    Text Solution

    |