Home
Class 12
MATHS
Without expanding the determinant at any...

Without expanding the determinant at any stage, find `K in R` such that
`|{:(4i,8+i,4+3i),(-8+i,16i,i),(-4+Ki,i,8i):}|` has purely imaginary value .

Text Solution

Verified by Experts

The correct Answer is:
3
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 4 (LEVEL -I) PREVIOUS YEAR - JEE MAIN|12 Videos
  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED|33 Videos
  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 2 (LEVEL -II) MULTIPLE CORRECT - JEE ADVANCED|10 Videos
  • CIRCLE

    MOTION|Exercise Exercise - 4 | Level - II (Previous Year | JEE Advanced|22 Videos
  • CONTINUITY

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) (PREVIOUS YEAR JEE ADVANCED)|5 Videos

Similar Questions

Explore conceptually related problems

Whitout expanding the determinat at any stage prove that |{:(-5,3+5i,(3)/(2)-4i),(3-5i,8,4+5i),((3)/(2)+4i,4-5i,9):}| has a purely real value.

If w=(z+4i)/(z+2i) is purely imaginary then find |z+3i|.

If z = |{:(-5,3+4i,5-7i),(3-4i,6,8+7i),(5+7i,8-7i,9):}| , then z is

if |(z-6)/(z+8)|=1 , then the value of x in R , where z=x+i|{:(-3,2i,2+i),(-2i,2,4-3i),(2-i,4+3i,7):}| , is

Let z!=i be any complex number such that (z-i)/(z+i) is a purely imaginary number.Then z+(1)/(z) is

Which term of the sequence 8-6i,7-4i,6-2i,...... is (i) purely real (ii) purely imaginary?

Prove that the value of the determinant |{:(-7,,5+3i,,(2)/(3)-4i),(5-3i ,,8,,4+5i),((2)/(3) +4i,,4-5i,,9):}|" is real "

MOTION-COMPLEX NUMBER -EXERCISE - 3 (LEVEL -III) SUBJECTIVE - JEE ADVANCED
  1. Show that the product [1+(1+i)/2][1+((1+i)/2)^2][1+((1+i)/2)^(2^2)]......

    Text Solution

    |

  2. Without expanding the determinant at any stage, find K in R such that ...

    Text Solution

    |

  3. Find the value of x and y which satisfy the following equations (x.y i...

    Text Solution

    |

  4. Find x and y if: (i) (x+iy) + (7-5i)=9+4i

    Text Solution

    |

  5. Given that x,yinR solve x^2-y^2-i(2x+y)=4i

    Text Solution

    |

  6. Given that x,y in R, solve (2 + 3i) x^2 - (3-2i)y = 2x - 3y + 5i

    Text Solution

    |

  7. Given that x,y in R : solve (4x^2+3xy)+(2xy-3x^2)iota=(4y^2-x^2/2)+(...

    Text Solution

    |

  8. The quadratic equation z^2 +(p+ip')z+q+iq' =0 where p,p',q,q' are all ...

    Text Solution

    |

  9. The quadratic equation z^2 +(p+ip')z+q+iq' =0 where p,p',q,q' are all ...

    Text Solution

    |

  10. Let z be a complex number satisfying the equation z^3-(3+i)z+m+2i=0,w ...

    Text Solution

    |

  11. If 2 and i are two roots of the equation 2z^4+az^3+bz^2+cz+3=0,where a...

    Text Solution

    |

  12. The real values of the parameter 'a' for which at least one complex nu...

    Text Solution

    |

  13. If |z1|=|z2|=dot=|zn|=1, prove that |z1+z2+z3++zn|=1/(z1)+1/(z2)+1/(z3...

    Text Solution

    |

  14. If alpha & beta are any two complex numbers, prove that |alpha+beta|...

    Text Solution

    |

  15. Prove that |alpha+sqrt(alpha^2-beta^2)|+|alpha-sqrt(alpha^2-beta^2)|= ...

    Text Solution

    |

  16. Prove the identity,|1-z1barz2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2)

    Text Solution

    |

  17. Among the complex numbers z satisfying the condition |z+3-sqrt(3)i|=sq...

    Text Solution

    |

  18. Given, z=cos.(2pi)/(2n+1)+i sin.(2pi)/(2n+1), 'n' a positive integer ...

    Text Solution

    |

  19. If alpha=e^(i2pi//7)a n df(x)=a0+sum(k-0)^(20)ak x^k , then prove that...

    Text Solution

    |

  20. Let alpha+ibeta,alpha, beta epsilon R, be a root of the equation x^(3)...

    Text Solution

    |