Home
Class 12
MATHS
Find the region on the Argand plane on w...

Find the region on the Argand plane on which z satisfies`1lt|z-2i|lt3`

Text Solution

Verified by Experts

Let`z=x+iy"The given inequality is "1lt|x+i(y-2)|lt 3`
`implies1lt sqrt(x^2+(y-2)^2 lt 3`
Promotional Banner

Topper's Solved these Questions

  • AREA UNDER PLANE CURVES (APPLICATION OF DEFINITE INTEGRALS)

    MBD PUBLICATION|Exercise QUESTION BANK|16 Videos

  • CONIC SECTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|179 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the plane Which contains the line of intersection of the planes x+2y+3z-4=0 and 2x+y-z+5=0 and perpendicular of the plane 5x+ 3y+6z+8=0 .

Find the equation of the plane passing through the line of intersection of the planes 2x+3y-z+1= 0 and x+y-2z+3= 0 , which is perpendicular to 3x-y-2z-4=0 .

Find the equation of the plane which passes through (1, 1, 2) and parallel to the plane x + 2y - z = 5.

Find the equation of the plane Passing through the intersection of planes 2x+3y-4z+1=0.2x-y+z+2=0 and passing through the point (3,2,1).

Find the equation of the plane passing through the intersection of the planes 2x + y + 3z-7=0 and 2x + 5y + 3z - 9 = 0 and the point (2,1,3).

Find the equation of the plane passing through the intersection of the planes 3x + y- z = 2 and x-y + 2z =1and the point (1, 0,2)

Find the equation of the plane Passing through the intersection of the planes x+3y-z+1=0 and 3x-y+5z+3=0 and is at a distance 2//3 units from origin.

MBD PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTION BANK
  1. Solve the equationz^3=1+i

    Text Solution

    |

  2. Given cos alpha+cos beta +cos gamma=sin alpha+sin beta +sin gamma=0 S...

    Text Solution

    |

  3. If sin alpha + sin beta +sin gamma=0 =cos alpha+cos beta+cos gamma=0 "...

    Text Solution

    |

  4. If x+1/x=2cos theta,"Show that"x^n+1/x^n=2cos n theta

    Text Solution

    |

  5. xr=cos alphar+isinalphar. r=1,2,3 "and" x1+x2+x3=0 "Show that" 1/x1+1...

    Text Solution

    |

  6. Show that ((1+sintheta+icostheta)/(1+sintheta-icostheta))^n =cos((npi)...

    Text Solution

    |

  7. If alpha "and" beta "are roots "x^2-2x+4=0 "then show that"alpha^n+bet...

    Text Solution

    |

  8. For a positive integer n show that (1+i)^n+(1-i)^n=2^((n+2)/2) "cos((n...

    Text Solution

    |

  9. For a positive integer n show that (1+isqrt3)^n+(1-isqrt3)^n=2^(n+1) "...

    Text Solution

    |

  10. Letx+1/x=2cos alpha, y+1/y=2cos beta z+1/z=2cosgamma."Show that"2 "co...

    Text Solution

    |

  11. Letx+1/x=2cos alpha, y+1/y=2cos beta z+1/z=2cosgamma."Show that"2 "co...

    Text Solution

    |

  12. Solve x^9+x^5-x^4=1

    Text Solution

    |

  13. Find the general value of theta" if"(cos theta+isintheta)("cos"2theta+...

    Text Solution

    |

  14. If z=x+iy"show that" |x|+|y|lesqrt2|z|

    Text Solution

    |

  15. Show thatRe(z1z2)=Rez1Rez2-Im z1Imz2 Im(z1z2)=Re z1 Im z2+Re z2 Im z1

    Text Solution

    |

  16. What is the value of arg omega+ arg omega^2?

    Text Solution

    |

  17. If |z1|le1,|z2|le1"show that" |1-z1z2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2...

    Text Solution

    |

  18. If z1^2+z2^2+z3^2-z2z3-z3z4=0 Show that |z1-z2|=|z2-z3|=|z3-z1|

    Text Solution

    |

  19. Solve ((1-i)x+3i)/(2+i)+((3+2i)y+i)/(2-i)=-i "where" x, y, in R.

    Text Solution

    |

  20. Find the region on the Argand plane on which z satisfies1lt|z-2i|lt3

    Text Solution

    |