Home
Class 11
MATHS
Let z and w be two non-zero complex numb...

Let z and w be two non-zero complex numbers such that ∣z∣=∣w∣ and arg(z)+arg(w)=π, then z equals

A

`pi/4`

B

`pi/2`

C

`(3pi)/4`

D

`(5pi)/4`.

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • LINEAR INEQUATIONS

    MODERN PUBLICATION|Exercise EXERCISE|289 Videos
  • LIMITS AND DERIVATIVES

    MODERN PUBLICATION|Exercise EXERCISE|334 Videos
  • MATHEMATICAL INDUCTION

    MODERN PUBLICATION|Exercise EXERCISE|85 Videos

Similar Questions

Explore conceptually related problems

If z and w are two non-zero complex numbers such that |zw|=1 and Arg (z) -Arg (w) =pi/2 , then bar z w is equal to :

Let z and w are two non zero complex number such that |z|=|w|, and Arg(z)+Arg(w)=pi then (a) z=w (b) z=overlinew (c) overlinez=overlinew (d) overlinez=-overlinew

Let z and w be two complex numbers such that |z|le1, |w|le1 and |z-iw|=|z-i bar w|=2 , then z equals :

If z_1a n dz_2 are two nonzero complex numbers such that |z_1+z_2|=|z_1|+|z_2|, then a rgz_1-a r g z_2 is equal to

If z_1=a + ib and z_2 = c + id are complex numbers such that |z_1|=|z_2|=1 and Re(z_1 bar z_2)=0 , then the pair of complex numbers omega_1=a+ic and omega_2=b+id satisfies a. |omega_(1)|=1 b. |omega_(2)|=1 c. Re(omega_(1)baromega_(2))=0 d. None of these

The number of complex numbers z such that |z-1|=|z+1|=|z-i| is

Numbers of complex numbers z, such that abs(z)=1 and abs((z)/bar(z)+bar(z)/(z))=1 is

Let alpha and beta be two fixed non-zero complex numbers and 'z' a variable complex number. If the lines alphabarz+baraz+1=0 and betabarz+barbetaz-1=0 are mutually perpendicular, then

Let z_(1),z_(2) and z_(3) be three non-zero complex numbers and z_(1) ne z_(2) . If |{:(abs(z_(1)),abs(z_(2)),abs(z_(3))),(abs(z_(2)),abs(z_(3)),abs(z_(1))),(abs(z_(3)),abs(z_(1)),abs(z_(2))):}|=0 , prove that (i) z_(1),z_(2),z_(3) lie on a circle with the centre at origin. (ii) arg(z_(3)/z_(2))=arg((z_(3)-z_(1))/(z_(2)-z_(1)))^(2) .

Let z_(1) and z_(2) be two distinct complex numbers and z=(1-t)z_(1)+tz_(2) , for some real number t with 0 lt t lt 1 and i=sqrt(-1) . If arg(w) denotes the principal argument of a non-zero complex number w, then a. abs(z-z_(1))+abs(z-z_(2))=abs(z_(1)-z_(2)) b. arg(z-z_(1))=arg(z-z_(2)) c. |{:(z-z_(1),bar(z)-bar(z)_(1)),(z_(2)-z_(1),bar(z)_(2)-bar(z)_(1)):}|=0 d. arg(z-z_(1))=arg(z_(2)-z_(1))

MODERN PUBLICATION-LINEAR INEQUATIONS-EXERCISE
  1. If |z|=1 and w=(z-1)/(z+1) (where z!=-1), then R e(w) is

    Text Solution

    |

  2. If z and w are two non-zero complex numbers such that |zw|=1 and Arg (...

    Text Solution

    |

  3. Let z and w be two non-zero complex numbers such that ∣z∣=∣w∣ and arg(...

    Text Solution

    |

  4. Let z =x-iy and z^(1/3)= p+iq.Then (x/p+y/q)//(p^2+q^2) is equal to:

    Text Solution

    |

  5. If |z^2-1|=|z|^2+1, then z lies on :

    Text Solution

    |

  6. If z1a n dz2 are two nonzero complex numbers such that |z1+z2|=|z1|+|z...

    Text Solution

    |

  7. If w= z/(z-i1/3) and |w|=1,then z lies on:

    Text Solution

    |

  8. If a, b, c and u, v, w are complex numbers representing the vertices o...

    Text Solution

    |

  9. If z^(2)+z+1=0, where z is a complex number, the value of (z+1/z)^(2)+...

    Text Solution

    |

  10. If omega=alpha+ibeta, " where " beta ne 0,i=sqrt(-1) " and " z ne 1, s...

    Text Solution

    |

  11. If abs(z+4) le 3, the maximum value of abs(z+1) is

    Text Solution

    |

  12. If |z|=1 and z!=1, then all the values of z/(1-z^2) lie on

    Text Solution

    |

  13. A man walks a distance of 3 units from the origin towards the North-...

    Text Solution

    |

  14. The conjugate of a complex number is 1/(i-1). Then that complex number...

    Text Solution

    |

  15. How many real solutions does the equation x^(7)=14x^(5)+16x^(3)+30x-56...

    Text Solution

    |

  16. The quadratic equations x^2""-6x""+""a""=""0""a n d ""x^2""-c x""+""...

    Text Solution

    |

  17. Let z=x+iy be a complex number, where x and y are integers and i=sqrt(...

    Text Solution

    |

  18. If |z-4/z|=2 then the greatest value of |z| is:

    Text Solution

    |

  19. If the roots of the equation b x^2+""c x""+""a""=""0 be imaginary, t...

    Text Solution

    |

  20. The number of complex numbersd z, such that abs(z-1)=abs(z+1)=abs(z-i)...

    Text Solution

    |