Home
Class 11
MATHS
a ,b ,c are three complex numbers on the...

`a ,b ,c` are three complex numbers on the unit circle `|z|=1,` such that `a b c=a+b+c dot` Then find the value of `|a b+b c+c a|dot`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

a ,b ,c are three complex numbers on the unit circle |z|=1, such that a b c=a+b+cdot Then find the value of |a b+b c+c a|dot

a , b , c are three complex numbers on the unit circle |z|=1 , such that abc=a+b+c . Then |ab+bc+ca| is equal to

If a+2b+3c=4, then find the least value of a^2+b^2+c^2dot

If a+2b+3c=4, then find the least value of a^2+b^2+c^2dot

If a b c=0 , then find the value of {(x^a)^b}^c (a)1 (b) a (c)b (d) c

Let a ,b and c be real numbers such that a+2b+c=4 . Find the maximum value of (a b+b c+c a)dot

If a ,b ,c ,d are four distinct positive numbers in G.P. then show that a+d > b+c dot

Let a , b , c , d be positive integers such that (log)_a b=3/2a n d(log)_c d=5/4dot If (a-c)=9, then find the value of (b-d)dot

if a,b,c are complex numbers such that a+b+c=0 and |a|=|b|=|c|=1 find the value of 1/a+1/b+1/c

If a, b, c are three non-zero numbers of the same sign, then the value of (a)/(b)+(b)/( c )+( c )/(a) lies in the interval

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If alpha!=betaa n dalpha^2=5alpha-3a n dbeta^2=5beta-3. find the equat...

    Text Solution

    |

  2. Express 1/(1-costheta+2isintheta) in the form x+i y .

    Text Solution

    |

  3. a ,b ,c are three complex numbers on the unit circle |z|=1, such that ...

    Text Solution

    |

  4. If alpha,beta are the roots of lthe equation 2x ^2-3x-6=0, find the eq...

    Text Solution

    |

  5. If z1, z2, z3 are distinct nonzero complex numbers and a ,b , c in R...

    Text Solution

    |

  6. If |z1|=15 and |z2-3-4i|=5,t h e n

    Text Solution

    |

  7. Determine the values o m for which equations 3x^2+4m x+2=0a n d2x^2+3x...

    Text Solution

    |

  8. If z=((sqrt(3)+i)^(17))/((1-i)^(50)) , then find a m p(z)dot

    Text Solution

    |

  9. A rectangle of maximum area is inscribed in the circle |z-3-4i|=1. If ...

    Text Solution

    |

  10. If alpha,beta are the roots of the equation a x^2+b x+c=0, then find t...

    Text Solution

    |

  11. If (3pi)/2 < alpha < 2pi then the modulus argument of (1+cos 2alpha)+i...

    Text Solution

    |

  12. The value of z satisfying the equation logz+logz^2+dot+logz^n=0 i s ...

    Text Solution

    |

  13. If the difference between the roots of the equation x^2+a x+1=0 is les...

    Text Solution

    |

  14. find the differtiation of (i) tan(secx) (ii) sin(tanx)

    Text Solution

    |

  15. Roots of the equation are (z+1)^5=(z-1)^5 are (a) +-itan(pi/5),+-ita...

    Text Solution

    |

  16. Find the value of a for which one root of the quadratic equation (a^2-...

    Text Solution

    |

  17. If |z1-z0|=|z2-z0|=a and amp((z2-z0)/(z0-z1))=pi/2 , then find z0

    Text Solution

    |

  18. Which of the following represents a points in an Argand pane, equidi...

    Text Solution

    |

  19. If the harmonic mean between roots of (5+sqrt(2))x^2-b x+8+2sqrt(5)=0i...

    Text Solution

    |

  20. If n in N >1 , then the sum of real part of roots of z^n=(z+1)^n is...

    Text Solution

    |