Home
Class 12
MATHS
If the imaginery part of (z-3)/(e^(ithet...

If the imaginery part of `(z-3)/(e^(itheta))+(e^(itheta))/(z-3)` is zero, then `z` can lie on

A

a straight line parallel to x-axis

B

a parabola

C

a circle of radius 1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    FIITJEE|Exercise EXERCISE 1|3 Videos

  • COMPLEX NUMBER

    FIITJEE|Exercise EXERCISE 2|3 Videos

  • COMPLEX NUMBER

    FIITJEE|Exercise SOLVED PROBLEMS (SUBJECTIVE)|20 Videos

  • CIRCLE

    FIITJEE|Exercise Numerical Based|2 Videos

  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

If Im((z-1)/(e^(theta i))+(e^(theta i))/(z-1))=0, then find the locus of z

If z= 5e^(itheta), then |e^(iz)| is equal to

If z=x+iy, x,y in R such that z!=1 and |z-1|!=1. If (z-1)/(e^((i pi)/(3)))+(e^((i pi)/(3)))/(z-1) is real, then locus of z is a straight line whose slope is

Let z be a non-zero complex number such that area of the triangle with vertices P(z), Q(ze^(pii//6)) and R(z(1+e^(pii//6))) is 0.64, then z lies on a circle of diameter ___________.

If (3)/(2+e^(itheta)) =ax + iby , then the locous of P(x,y) will represent

Read the following writeup carefully: In argand plane |z| represent the distance of a point z from the origin. In general |z_1-z_2| represent the distance between two points z_1 and z_2 . Also for a general moving point z in argand plane, if arg(z) =theta , then z=|z|e^(itheta) , where e^(itheta) = cos theta + i sintheta . Now answer the following question If |z-(3+2i)|=|z cos ((pi)/(4) - "arg" z)|, then locus of z is

FIITJEE-COMPLEX NUMBER-SOLVED PROBLEMS (OBJECTIVE)
  1. If a is a positive integer, z = a +2i and z|z| - az +1=0 then

    Text Solution

    |

  2. If alpha is the angle which each side of a regular polygon of n sides ...

    Text Solution

    |

  3. If the imaginery part of (z-3)/(e^(itheta))+(e^(itheta))/(z-3) is zero...

    Text Solution

    |

  4. The distance of the roots of the equation tan theta(0) z^(n) + tan the...

    Text Solution

    |

  5. The complex numbers z=x+iy which satisfy the equation |(z-5i)/(z+5i)|=...

    Text Solution

    |

  6. The inequality |z-4| lt |z-2| represents

    Text Solution

    |

  7. If the equation |z-z1|^2 + |z-z2|^2 =k, represents the equation of a c...

    Text Solution

    |

  8. If |z|= "min" {|z-1|, |z+1|}, then

    Text Solution

    |

  9. The range of m for which the line z(1-mi) - bar(z) (1+mi)=0 divides tw...

    Text Solution

    |

  10. Let P(k)(k=1,2,…n) be the nth root of unity. Let z =a +ib and A(k) = R...

    Text Solution

    |

  11. A complex number z is rotated in anticlockwise direction by an angle ...

    Text Solution

    |

  12. one vertex of the triangle of maximum area that can be inscribed in th...

    Text Solution

    |

  13. Let 'z' be a complex number and 'a' be a real parameter such that z^2+...

    Text Solution

    |

  14. Roots of the equation x^n - 1 = 0, n in I

    Text Solution

    |

  15. Let z(1) and z(2) be complex numbers such that z(1)^(2)-4z(2)=16+20i a...

    Text Solution

    |

  16. Let z(1) and z(2) be complex numbers such that z(1)^(2)-4z(2)=16+20i a...

    Text Solution

    |

  17. Let z1 and z2 be complex numbers such that z(1)^(2) - 4z(2) = 16+20i a...

    Text Solution

    |

  18. The locus of any point P(z) on argand plane is arg((z-5i)/(z+5i))=(pi)...

    Text Solution

    |

  19. The locus of any point P (z) on argand plane is "arg" ((z+5i)/(z-5i))=...

    Text Solution

    |

  20. If |z- z1|^2 + |z-z-2|^2 = |z1 - z2|^2 represents a conic C, then for...

    Text Solution

    |