Home
Class 12
MATHS
Consider the region R in the Argand plan...

Consider the region `R` in the Argand plane described by the complex number. `Z` satisfying the inequalities `|Z-2| le |Z-4|`, `|Z-3| le |Z+3|`, `|Z-i| le |Z-3i|`, `|Z+i| le |Z+3i|`
Answer the followin questions :
The maximum value of `|Z|` for any `Z` in `R` is

A

`5`

B

`3`

C

`1`

D

`sqrt(13)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `|Z-2| le |Z-4|implies|Z-2|^(2) le |Z-4|^(2)`
`implies (x-2)^(2)+y^(2) le (x-4)^(2)+y^(2)`
`implies8x-4x le 16-4`
`impliesx le 3`
`|Z-3| le |Z+3| implies x ge 0`
`|Z-i| le |Z-3i| implies y le 2`
`|Z+i| le |Z+3i| implies y ge -2`
So, `z` lies on or inside rectangle formed by lines `x=0`, `x=3`, `y=-2` and `y=2`.
`(1)` Max of `|Z|=OC` or `OB=sqrt(3^(2)+2^(2))=sqrt(13)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Examples|125 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.1|4 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Matching Column|1 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

Consider the region R in the Argand plane described by the complex number. Z satisfying the inequalities |Z-2| le |Z-4| , |Z-3| le |Z+3| , |Z-i| le |Z-3i| , |Z+i| le |Z+3i| Answer the followin questions : Minimum of |Z_(1)-Z_(2)| given that Z_(1) , Z_(2) are any two complex numbers lying in the region R is

IF |z+4|le3, then the maximum value of |z+1| is

If |z + 3| le 3 then find minimum and maximum values of |z|

Let Z be a complex number satisfying |Z-1| <= |Z-3|, |Z-3| <= |Z-5|, |Z+ i| <= |Z- i|, |Z- i| <= |Z- 5i|. Then area of region in which Z lies is A square units, Where A is equal to :

Locate the region in the argand plane for z satisfying |z+i|=|z-2|.

If |z + 3| le 3 then find minimum and maximum values of |z-1|

If |z + 3| le 3 then find minimum and maximum values of |z+1|

If |z-3i| ltsqrt5 then prove that the complex number z also satisfies the inequality |i(z+1)+1| lt2sqrt5 .