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 :
Maximum of `|Z_(1)-Z_(2)|` given that `Z_(1)`, `Z_(2)` are any two complex numbers lying in the region `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 PUBLICATION|Exercise ILLUSTRATION|110 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise SLOVED EXAMPLES|15 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Matching Column|1 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 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

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

The complex number z satisfying the equation |z-i|=|z+1|=1 is

The complex number z satisfying the question |(i -z)/(i+z)|=1 lies on-

Find the complex number z satisfying R e(z^2) =0,|z|=sqrt(3.)

If the complex number z satisfies the equations |z-12|/|z-8i|=(5)/(3) and |z-4|/|z-8| =1, "find" z.

Let z be a complex number satisfying |z+16|=4|z+1| . Then

The complex number z satisfies z+|z|=2+8i . find the value of |z|-8

The maximum value of |z| when the complex number z satisfies the condition |z+(2)/(z)|=2 is -

If z be a complex number satisfying z^4+z^3+2z^2+z+1=0 then absz is equal to