Home
Class 12
MATHS
If is any complex number such that |z+4|...

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

Text Solution

Verified by Experts

The correct Answer is:
6
`|z + 1 | = |z + 4 - 3 |`
` = |( z + 4) + (-3)|` ltBrgt ` le |z + 4| + |-3|`
` = |z + 4| + 3 `
` le 3 + 3 = 6" " [ because |z + 4| le 3]`
Hence, the greatest value of ` |z + 1 |` is 6.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.9|8 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.10|10 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.7|6 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

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

If z is a any complex number such that |z+4|le3, find the greatest value of |z+1|.

If |z^2-4|=2|z| then find the greatest value of |z|.

If |z+4|<=3 then find the greatest and least values of |z+1|

If z is any complex number such that |3z-2|+|3z+2|=4, then identify the locus of z

If z is a complex number such that |z|>=2 then the minimum value of |z+(1)/(2)| is

Let z be a complex number such that |z|=5 Find the maximum value of |z+3+4i|

If z be a complex number satisfying |z-4+8i|=4 , then the least and the greatest value of |z+2| are respectively (where i=sqrt(-i) )

If z is a complex number satisfying |z^(2)+1|=4|z| , then the minimum value of |z| is