Home
Class 12
MATHS
If z1, z2 are the non zero complex root...

If `z_1, z_2` are the non zero complex root of `z^2 -ax + b=0` such that `|z_1| =|z_2|`, where a, b arecomplex numbers. If `A(z_1), B(z_2) and /_AOB =theta, 'O'` being the origin, then prove `a^2=4b cos^2 (theta/2)`

A

`a^(2)=4b cos^(2)(theta)/(2)`

B

`b^(2)=4a cos^(2)""(theta)/(2)`

C

`b^(2)=2a cos^(2)""(theta)/(2)`

D

`a^(2)=2b cos^(2)""(theta)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICS TIPS

    FIITJEE|Exercise ASSIGNMENT -OBJECTIVE|84 Videos

  • MATHEMATICS TIPS

    FIITJEE|Exercise ASSERTION - REASONING|8 Videos

  • MATHEMATICS TIPS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|21 Videos

  • MATHEMATICS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|15 Videos

  • MATRICES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

If z_(1),z_(2) are the non zero complex root of z^(2)-ax+b=0 such that |z_(1)|=|z_(2)|, where a,b arecomplex numbers.If A(z_(1)),B(z_(2)) and /_AOB=theta,'O' being the origin,then prove a^(2)=4b cos^(2)((theta)/(2))

z_(1) and z_(2) are the roots of the equaiton z^(2) -az + b=0 where |z_(1)|=|z_(2)|=1 and a,b are nonzero complex numbers, then

Let Z_1 and Z_2 are two non-zero complex number such that |Z_1+Z_2|=|Z_1|=|Z_2| , then Z_1/Z_2 may be :

If z_1 and z_2 are two distinct non-zero complex number such that |z_1|= |z_2| , then (z_1+ z_2)/(z_1 - z_2) is always

If z_1 and z_2 are two complex numbers such that |z_1|lt1lt|z_2| then prove that |(1-z_1barz_2)/(z_1-z_2)|lt1

If z_1 and z_2 are two non zero complex number such that |z_1+z_2|=|z_1|+|z_2| then arg z_1-argz_2 is equal to (A) - pi/2 (B) 0 (C) -pi (D) pi/2

If z_1,z_2 are nonzero complex numbers then |(z_1)/(|z_1|)+(z_2)/(|z_2|)|le2 .

Let z_(1) and z_(2) be two non-zero complex number such that |z_(1)|=|z_(2)|=|(1)/(z_(1)+(1)/(z_(2)))|=2 What is the value of |z_(1)+z_(2)| ?

FIITJEE-MATHEMATICS TIPS-ASSIGNMENT (SECTION (I) : MCQ (SINGLE CORRECT)
  1. If z(0) is one of the roots of the equation z^(n)cos theta(0)+z^(n-1)c...

    Text Solution

    |

  2. A(z1),B(z2) and C(z3) are the vertices of triangle ABC inscribed in th...

    Text Solution

    |

  3. If z1, z2 are the non zero complex root of z^2 -ax + b=0 such that |...

    Text Solution

    |

  4. If (1+3+5++p)+(1+3+5++q)=(1+3+5++r) where each set of parentheses cont...

    Text Solution

    |

  5. h1. If C is skew-symmetric matrix of order n and X is nxx1 column matr...

    Text Solution

    |

  6. If A=[(1,2),(2,1)] and f(x)=(1+x)/(1-x), then f(A) is

    Text Solution

    |

  7. Let there is an A.P. with common difference 4 such that the squares of...

    Text Solution

    |

  8. If P is a two-rowed matrix satisfying P' = P^(-1), then P can be

    Text Solution

    |

  9. For A=[{:(4,2i),(i,1):}],(A-2l)(A-3l) is a

    Text Solution

    |

  10. If square matrices A and B are such that "AA"^(theta),"BB"^(theta)=B^(...

    Text Solution

    |

  11. Matrix A has x rows and x+5 columns. Matrix B has y rows and 11-y colu...

    Text Solution

    |

  12. If A^(k)=0 (null matrix) for some value of k, then l+A+A^(2)+…A^(k-1) ...

    Text Solution

    |

  13. If A is the n xx n matrix whose elements are all '1' and B is the n xx...

    Text Solution

    |

  14. If M is a 3xx3 matrix, where det M=1a n dM M^T=1,w h e r eI is an iden...

    Text Solution

    |

  15. if A=[{:(alpha,2),(2, alpha):}] and |A^(3)|=125 then the value of alph...

    Text Solution

    |

  16. Let A=[1 0 0 0 1 1 0-2 4],I=[1 0 0 0 1 0 0 0 1]a n dA^(-1)=[1/6(A^2+c ...

    Text Solution

    |

  17. for A=[{:(4,2i),(i,1):}],(A-2l)(A-3l) is a

    Text Solution

    |

  18. If |(a,b,aalpha+b),(b,c,balpha+c),(a alpha+b,b alpha+c,0)|=0 then

    Text Solution

    |

  19. Let f(x) = |{:(secx,cosx,sec^(2)x+cotx cosecx),(cos^(2)x,cos^(2)x,cose...

    Text Solution

    |

  20. The square of sum of the roots of the equation x^(3)+2x^(2)+2x+1=0 equ...

    Text Solution

    |