Home
Class 11
MATHS
If z=2-3i show that z^2=4z+13=0 and henc...

If `z=2-3i` show that `z^2=4z+13=0` and hence find the value of `4z^3-3z^2+169.`

Text Solution

Verified by Experts

The correct Answer is:
0
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CBSE COMPLEMENTARY MATERIAL|Exercise Very Short Answer Type Questions(True or False|5 Videos

  • BINOMIAL THEOREM

    CBSE COMPLEMENTARY MATERIAL|Exercise LONG ANSWER TYPE QUESTIONS(Section-D)|16 Videos

  • COORDINATE GEOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise section(D) (Long Answer Type Questions ) (6 Marks)|21 Videos

Similar Questions

Explore conceptually related problems

If z=2-3i, then show that z^(2)-4z+13=0 .

If z=1+2i , show that z^(2)-2z+5=0 . Hence find the value of z^(3) +7z^(2)-z+16 .

If z=2-3i, value of 4z^(3)-3z^(2)+169 will be

If z=4+i sqrt(7), then find the value of z^(2)-4z^(2)-9z+91

If z = 3 + 2i , prove that z^(2) - 6z + 13 = 0 and hence deduce that 3z^(3) - 13z^(2) + 9z + 65 = 0 .

If z = -5 + 3i , find the value of (z^(4)+9z^(3)+26z^(2)-14z + 8) .

If z_1 = 3i and z_2 = -1 -i , find the value of arg z_1/z_2 .

If z = 3-5i then show that z^3 -10z^2+58z -136=0

If z=(1)/(2)(i sqrt(3)-1), then find the value of (z-z^(2)+2z^(3))(2-z+z^(2))

If z = 3-5i then show that z^3 - 10z^2 +58z-136=0

CBSE COMPLEMENTARY MATERIAL-COMPLEX NUMBERS AND QUADRATIC EQUATIONS -Short Answer Type Questions
  1. Find the real value of x and y if ((1+i)x-2i)/(3+i)+((2-3i)y+i)/(3-i)...

    Text Solution

    |

  2. If (1+i)(1+2i)(1+3i)(1+n i)=(x+i y) , show tht 2. 5. 10 (1+n^2)=x^2+y^...

    Text Solution

    |

  3. If z=2-3i show that z^2=4z+13=0 and hence find the value of 4z^3-3z^2+...

    Text Solution

    |

  4. If ((1+i)/(1-i))^3-((1-i)/(1+i))^3 =a+ib find a and b

    Text Solution

    |

  5. For complex numbers z1 = 6+3i, z2=3-I find (z1)/(z2)

    Text Solution

    |

  6. If ((2+2i)/(2-2i))^(n)=1 find the least positive integral of n.

    Text Solution

    |

  7. if (x+i y)^(1/3) = a+ib then (x/a) + (y/b) equals to

    Text Solution

    |

  8. Convert the following in polar form, (i)-3sqrt2+3sqrt2i

    Text Solution

    |

  9. Convert the following in polar form, (ii) ((sqrt3 -1)-(sqrt3+1)i)/((2s...

    Text Solution

    |

  10. Convert the following in polar form, (iii)i(1+i)

    Text Solution

    |

  11. Convert the following in polar form, (iv)(5-i)/(2-3i)

    Text Solution

    |

  12. Solve (i) x^(2) -(3sqrt2-2i)x-6sqrt2i=0

    Text Solution

    |

  13. Solve the following equations by using the general expression for a qu...

    Text Solution

    |

  14. Find the square root of 7-30Sqrt(-2)

    Text Solution

    |

  15. Prove that: x^4=4=(x+1+i)(x+1-i)(x-1+i(x-1-i)dot)

    Text Solution

    |

  16. Show that |(z -2)/(z - 3)| = 2 represents a circle, find its centre ...

    Text Solution

    |

  17. Find all non zero complex numbers z satisfying barz=iz^2

    Text Solution

    |

  18. If i z^3+z^2-z+i=0 , where i=sqrt(-1) , then |z| is equal to 1 (b) 1/2...

    Text Solution

    |

  19. If z1,z2 are complex numbers such that, (2z1)/(3z2) is purely imaginar...

    Text Solution

    |

  20. If z1 and z2 are complex numbers such that, |1-bar z1z2|^(2)-|z1-z(2^(...

    Text Solution

    |