Home
Class 12
MATHS
P represents the variable complex number...

P represents the variable complex number z. Find the locus of P, if `Im ((2z + 1)/(iz + 1)) = -2`.

Text Solution

Verified by Experts

The correct Answer is:
`x + 2y - 2 = 0`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.1|6 Videos

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.2|3 Videos

  • COMPLEX NUMBERS

    FULL MARKS|Exercise EXERCISE - 2.9|25 Videos

  • APPLICATIONS OF VECTOR ALGEBRA

    FULL MARKS|Exercise Additional Questions Solved|59 Videos

  • DIFFERENTIALS AND PARTIAL DERIVATIVES

    FULL MARKS|Exercise Additional Questions Solved|29 Videos

Similar Questions

Explore conceptually related problems

Investigate for what values of lambda and mu the system of linear equations. x + 2y + z = 7, x + y + lambda z = mu , x + 3y - 5z = 5 . Has (i) no solution (ii) a unique solution (iii) an infinte number of solutions. (b) P prpresents the variable complex number z. Find the locus of P , if Re ((z+1)/(z+i)) = 1 .

P represents the variable complex number z find the locus of z if : Re((z+1)/(z+i))=1

Represents the variable complex number z . Find the locus of P if arg((z-1)/(z+3))=(pi)/(2) .

Represent the complex number z=1+isqrt(3) in the polar form.

If z= x+iy find the locus of z if |2z+1| = 2 .

If |z-1|=2 then the locus of z is

The locus of z such that |(1+iz)/(z+i)|=1 is

If z is any complex number, then the points z,iz,-z,-iz

Find the correct staements in the following? If P represents the complex number z and if |2z-1|=2|z| then the locus of z .

FULL MARKS-COMPLEX NUMBERS -ADDITIONAL QUESTIONS SOLVED
  1. Show that |(z-3)/(z + 3)| = 2 represent a circle

    Text Solution

    |

  2. If arg(z - 1) = pi/6 and arg(z + 1) = 2 pi/3 , then prove that |z| = 1...

    Text Solution

    |

  3. P represents the variable complex number z. Find the locus of P, if Im...

    Text Solution

    |

  4. P represents the variable complex number z find the locus of z if : ...

    Text Solution

    |

  5. Write the following complex numbers in the polar form : 1- i

    Text Solution

    |

  6. Find the modulus and principal argument of (1 + i) and hence express i...

    Text Solution

    |

  7. Express the following complex numbers in the polar form. (i) (1 + i)...

    Text Solution

    |

  8. Express the following complex numbers in the polar form : 2 + sqrt(3) ...

    Text Solution

    |

  9. Find the modulus and principal argument of the following complex numbe...

    Text Solution

    |

  10. Express the following complex numbers in the polar form : -1 - i

    Text Solution

    |

  11. Express the following complex numbers in the polar form : 1 - i

    Text Solution

    |

  12. Evaluate i^(50)

    Text Solution

    |

  13. Evaluate i^(59)

    Text Solution

    |

  14. Prove that : (1 + i)^(4n) and (1 + i)^(4n + 2) are real and purely ima...

    Text Solution

    |

  15. If x = cos alpha + i sin alpha , y = cos beta + i sin beta, prove that...

    Text Solution

    |

  16. If a = cos 2alpha + i sin 2 alpha, b = cos 2 beta + i sin 2 beta and c...

    Text Solution

    |

  17. Solve : x^4 + 4 = 0

    Text Solution

    |

  18. If x = a + b, y = a omega + b omega^2, z = aomega^2 + b omega, show th...

    Text Solution

    |

  19. ((1 - i)/(1+ i))^(100) = a + ib then (a,b) is ……….

    Text Solution

    |

  20. If ((1 + i)/(1 - i))^(3) - ((1 - i)/(1 + i))^(3) = x + iy then (x, y) ...

    Text Solution

    |