Home
Class 12
MATHS
Suppose that z is a complex number the s...

Suppose that `z` is a complex number the satisfies `|z-2-2i|lt=1.` The maximum value of `|2i z+4|` is equal to _______.

Text Solution

Verified by Experts

The correct Answer is:
3
`|z-2-2i| le 1`
denotes the region inside a circle with center (2,2) and radius is 1.

`|2iz + 4|=|2i(z-2i)|`
`=|2i| |z-2i|`
`= 2|z-2i|`
`|z-2i|`= distance of z form `P(0,2)`
Hence,maximum value is 3.
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise ARCHIVES (SINGLE CORRECT ANSWER TYPE )|11 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise LINKED COMPREHENSION TYPE|36 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|101 Videos

Similar Questions

Explore conceptually related problems

Suppose that z is a complex number the satisfies |z-2-2i|lt=1. The maximum value of |2z-4i| is equal to _______.

If z is any complex number satisfying |z-3-2i|lt=2 then the maximum value of |2z-6+5i| is

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

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

If z is a complex number satisfying ∣z 2 +1∣=4∣z∣, then the minimum value of ∣z∣ is

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

For the complex number z satisfying the condition |z+(2)/(z)|=2 , the maximum value of |z| is

Let z be a complex number satisfying |z-5i|<=1 such that amp(z) is minimum, then z is equal to

If for the complex number z satisfying Іz-2-2i І ≤ 1, the maximum value of І3iz+6І is attained at a+ib then a+b=

If z=x+iy is a complex number satisfying |z+i/2|^2=|z-i/2|^2 , then the locus of z is

CENGAGE ENGLISH-COMPLEX NUMBERS-NUMERICAL VALUE TYPES
  1. Let 1,,w^2 be the cube root of unity. The least possible degree of a p...

    Text Solution

    |

  2. If omega is the imaginary cube roots of unity, then the number of p...

    Text Solution

    |

  3. Suppose that z is a complex number the satisfies |z-2-2i|lt=1. The max...

    Text Solution

    |

  4. If |z+2-i|=5 and maxium value of |3z +9-7i| is M, then the value of M ...

    Text Solution

    |

  5. Let Z1 = (8 + i)sin theta + (7 + 4i)cos theta and Z2 = (1 + 8i)sin th...

    Text Solution

    |

  6. Let A={a in R} the equation (1+2i)x^3-2(3+i)x^2+(5-4i)x+a^2=0 has at ...

    Text Solution

    |

  7. Find the minimum value of the expression E= |z|^2+ |z-3|^2 + |z- 6i|^2...

    Text Solution

    |

  8. If z1 lies on |z-3| + |z + 3| = 8 such that arg z1 = pi//6 , ...

    Text Solution

    |

  9. If z satisfies the condition arg(z + i) = (pi)/(4) . Then the ...

    Text Solution

    |

  10. Let omega ne 1 be a complex cube root of unity. If ( 4 + ...

    Text Solution

    |

  11. Let z be a non - real complex number which satisfies the equatio...

    Text Solution

    |

  12. If z, z 1 and z2 are complex numbers such that z = z 1 z2 ...

    Text Solution

    |

  13. Let z1 , z 2 and z3 be three complex numbers such that z1 + z2+ ...

    Text Solution

    |

  14. Let alpha be the non-real 5 th root of unity. If z1 and z2...

    Text Solution

    |

  15. Let z1, z2 , z3 in C such that |z1 | = |z2| = |z3| = |z1+ z...

    Text Solution

    |

  16. Let A (z1 ) and B(z2 ) be lying on the curve |z-3 - 4i| = 5, w...

    Text Solution

    |

  17. If z1,z2,z3 are three points lying on the circle |z|=2 then the minimu...

    Text Solution

    |

  18. Minimum value of |z1 + 1 | + |z2 + 1 | + |z 1 z 2 + 1 | i...

    Text Solution

    |

  19. If |z 1 |= 2 and (1 - i)z2 + (1+i)barz2 = 8sqrt2, then the mi...

    Text Solution

    |

  20. Given that 1 + 2|z|^(2) = |z^(2) + 1|^(2) + 2 | z + 1 | ^(2), t...

    Text Solution

    |