Home
Class 11
MATHS
If z1a n dz2 both satisfy z+barz r =2|...

If `z_1a n dz_2` both satisfy `z+barz r =2|z-1| and a r g(z_1-z_2)=pi/4` , then find I m(z_1+z_2) .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMBINATIONS

    RD SHARMA ENGLISH|Exercise All Questions|117 Videos
  • DERIVATIVES

    RD SHARMA ENGLISH|Exercise All Questions|230 Videos

Similar Questions

Explore conceptually related problems

If z_1a n dz_2 both satisfy z+ z =2|z-1| and a r g(z_1-z_2)=pi/4 , then find I m(z_1+z_2) .

If |z_(1)|=|z_(2)| and arg (z_(1)//z_(2))=pi, then find the of z_(1)z_(2).

If |z_1-z_0|=z_2-z_1=pi/2 , then find z_0 .

If z_(1) and z_(2) satisfy the equation |z-2|=|"Re"(z)| and arg (z1-z2)=pi/3, then Im (z1+z2) =k/sqrt 3 where k is

If z_1=2-i ,\ z_2=-2+i , find : Im(1/(z_1bar(z_2))) .

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( z )_2dot

Let z_1a n dz_2 be two complex numbers such that ( z )_1+i( z )_2=0 and arg(z_1z_2)=pidot Then, find a r g(z_1)dot

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=- bar z _2dot

if z_(1)=1-i and z_(2) = -2 + 4i then find Im((z_(1)z_(2))/barz_(1))

if z_(1) = 3i and z_(2) =1 + 2i , then find z_(1)z_(2) -z_(1)

RD SHARMA ENGLISH-COMPLEX NUMBERS-All Questions
  1. Let z1a n dz2 be two complex numbers such that ( z )1+i( z )2=0 and ...

    Text Solution

    |

  2. If |z-5i|=|z+5i| , then the locus of zdot

    Text Solution

    |

  3. If z1a n dz2 both satisfy z+barz r =2|z-1| and a r g(z1-z2)=pi/4 , t...

    Text Solution

    |

  4. Show that the complex number z, satisfying the condition arg ((z -1)/(...

    Text Solution

    |

  5. If z=(1+7i)/((2-i)^2) , then find |z|?

    Text Solution

    |

  6. The value of (i^5+i^6+i^7+i^8+i^9)/(1+i) is

    Text Solution

    |

  7. Write the least positive integral value of n for which ((1+i)/(1-i))^n...

    Text Solution

    |

  8. If f(z)=(7-z)/(1-z^2) , where z=1+2i , then |f(z)| is

    Text Solution

    |

  9. If z1,z2, z3 are complex numbers such that |z1|=|z2|=|z3|=|1/z1+1/z2+1...

    Text Solution

    |

  10. What is the locus of z , if amplitude of (z-2-3i) is pi/4?

    Text Solution

    |

  11. Write the sum of the series i+i^2+i^3+....... upto 1000 terms.

    Text Solution

    |

  12. The sum and product of two complex numbers are real if and only if the...

    Text Solution

    |

  13. If ((a+i)^2)/((2a-i))=p+i q , show that: p^2+q^2=((a^2+1)^2)/((4a^2+1)...

    Text Solution

    |

  14. Write the value of a r g(z)+a r g(barz ) .

    Text Solution

    |

  15. Express the following complex numbers in the standard form. Also find ...

    Text Solution

    |

  16. Find the conjugate of 1/(3+4i)dot

    Text Solution

    |

  17. If under root of (a+i b)/(c+i d)=x+i y , Prove (a^2+b^2)/(c^2+d^2)=(x...

    Text Solution

    |

  18. Find real values of x and y for which the complex numbers -3+i x^2y ...

    Text Solution

    |

  19. Find the real values of x and y for which (1+i)y^2+(6+i)=(2+i)x

    Text Solution

    |

  20. Find the real values of xa n dy , if (3x-7)+2i y=-5y+(5+x)i

    Text Solution

    |