Home
Class 12
MATHS
If z is a complex number such that |z -...

If z is a complex number such that `|z - barz| +|z + barz| = 4` then find the area bounded by the locus of z.

Text Solution

Verified by Experts

We have `|z - bar z| +|z + barz|= 4`
`therefore " " |2iy| +|2x|= 4`
` rArr |x| +|y|=2`

This equation forms square with vertices `(pm 2,0)` and `(0, pm2)`
so, area of square is 8 sq.units
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise SLOVED EXAMPLES|15 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise EXERCISE3.1|4 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

Similar Questions

Explore conceptually related problems

If z is any complex number such that |z+4|lt=3, then find the greatest value of |z+1|dot

If z is a complex number such taht z^2=( barz)^2, then find the location of z on the Argand plane.

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

If z be any complex number such that abs(3z-2)+abs(3z+2)=4 then locus of z is

z is a complex number. The minimum value of |z | + I z - 2| is

If z=4+3i, then find z-barz

If z=4-3i, then find z-barz

If omega is any complex number such that z omega=|z|^(2) and |z-barz|+|omega+baromega|=4 , then as omega varies, then the area bounded by the locus of z is

The number of complex numbers z such that |z|=1 and |z/ barz + barz/z|=1 is arg(z) in [0,2pi)) then a. 4 b. 6 c. 8 d. more than 8

If z=6-i, then find z-barz

CENGAGE PUBLICATION-COMPLEX NUMBERS-ILLUSTRATION
  1. Find real q such that (3+2isintheta)/(1-2isintheta) is purely real.

    Text Solution

    |

  2. If the imaginary part of (2z+1)//(i z+1) is -2, then find the locus of...

    Text Solution

    |

  3. If z is a complex number such that |z - barz| +|z + barz| = 4 then fi...

    Text Solution

    |

  4. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

    Text Solution

    |

  5. If z = x + iy lies in the third quadrant, then prove that (barz)/(z) ...

    Text Solution

    |

  6. Let z = ((sqrt(3))/(2) + (i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5). If ...

    Text Solution

    |

  7. Find the relation if z1, z2, z3, z4 are the affixes of the vertices of...

    Text Solution

    |

  8. Let z1, z2, z3 be three complex numbers and a ,b ,c be real numbers no...

    Text Solution

    |

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

    Text Solution

    |

  10. about to only mathematics

    Text Solution

    |

  11. If (x+i y)^3=u+i v ,then show that u/x+v/y=4(x^2-y^2).

    Text Solution

    |

  12. Let z be a complex number satisfying the equation z^2-(3+i)z+m+2i=0,w ...

    Text Solution

    |

  13. Show that the equation Z^4+2Z^3+3Z^2+4Z+5=0 has no root which is eithe...

    Text Solution

    |

  14. Find the square root of the following: 5+12 i

    Text Solution

    |

  15. Evaluate : i^(135)

    Text Solution

    |

  16. Solve for z : z^2-(3-2i)z=(5i-5)dot

    Text Solution

    |

  17. Solve the equation (x-1)^3+8=0 in the set C of all complex numbers.

    Text Solution

    |

  18. If n is n odd integer that is greater than or equal to 3 but not a mul...

    Text Solution

    |

  19. omega is an imaginary root of unity. Prove that If a+b+c = 0 th...

    Text Solution

    |

  20. Find the complex number omega satisfying the equation z^3-8i and lying...

    Text Solution

    |