Home
Class 12
MATHS
If f(z) = a0z^n+a1z^(n-1)+a2z^(n-2)+...+...

If f(z) = `a_0z^n+a_1z^(n-1)+a_2z^(n-2)+...+a_n` where z is a complex number and `a_1 , a_2` , etc , are real , prove that `barf(z)=f(barz)` .

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    A DAS GUPTA|Exercise EXERCISE|224 Videos

  • Circular Functions, Identities

    A DAS GUPTA|Exercise Exercise|300 Videos

  • Continuity, Differentiability and Graph of Function

    A DAS GUPTA|Exercise Exercise|38 Videos

Similar Questions

Explore conceptually related problems

Prove that |(z-1)/(1-barz)|=1 where z is as complex number.

If z is a complex number of unit modulus and argument theta , then the real part of (z(1-barz))/(barz(1+z)) , is

If z_(1) and z_(2) are two complex numbers such that |z_(1)| lt 1 lt |z_(2)| , then prove that |(1- z_(1)barz_(2))//(z_(1)-z_(2))| lt 1

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

Let z_1, z_2 be two complex numbers with |z_1| = |z_2| . Prove that ((z_1 + z_2)^2)/(z_1 z_2) is real.

If |Z-2|=2|Z-1| , then the value of (Re(Z))/(|Z|^(2)) is (where Z is a complex number and Re(Z) represents the real part of Z)

If z is a complex number satisfying z+z^(-1)=1 then z^(n)+z^(-n),n in N, has the value

For two complex numbers z_(1) and z_(2) , we have |(z_(1)-z_(2))/(1-barz_(1)z_(2))|=1 , then

If z_1, z_2 be the complex numbers satisfying x^2 +4=2x, prove that z_1^n+z_2^n=2^(n+1) cosfrac(npi)(3) .

A DAS GUPTA-COMPLEX NUMBERS-EXERCISE
  1. If the complex numbers z1, z2,.......zn lie on te unit circle |z| = 1 ...

    Text Solution

    |

  2. Show that if iz^3+z^2-z+i=0, then |z|=1

    Text Solution

    |

  3. If f(z) = a0z^n+a1z^(n-1)+a2z^(n-2)+...+an where z is a complex numbe...

    Text Solution

    |

  4. If |z1+z2| = |z1-z2|, prove that ampz1 - ampz2 = pi/2 .

    Text Solution

    |

  5. Prove that |z1+z2|^2 = |z1|^2+|z2|^2 if z1/z2 is purely imaginary.

    Text Solution

    |

  6. Prove that |z1+z2|^2+|z1-z2|^2 =2|z1|^2+2|z2|^2.

    Text Solution

    |

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

    Text Solution

    |

  8. Prove that |1-barz1z2|^2-|z1-z2|^2=(1-|z1|^2)(1-|z2|^2).

    Text Solution

    |

  9. If |z-1| <3, prove that |iz+3-5i| < 8.

    Text Solution

    |

  10. Prove that for nonzero complex numbers |z1+z2| |frac(z1)(|z1|)+frac(z2...

    Text Solution

    |

  11. Prove that following inequalities: (i) |(z)/(|z|) -1| le |arg z| (...

    Text Solution

    |

  12. Find the value of w^4+w^6+w^8, if w is a complex cube root of unity.

    Text Solution

    |

  13. Find the range of real number alpha for which the equation z+alpha|z-1...

    Text Solution

    |

  14. If a, b are real, prove that the equation z^2+az+b=0 will not have any...

    Text Solution

    |

  15. Find the maximum and minimum values of |z| satisfying |z+(1)/(z)|=2

    Text Solution

    |

  16. If |z|ge3, then determine the least value of |z+(1)/(z)|.

    Text Solution

    |

  17. If z is a complex number such that |z+1/z|=1 show that Re(z)=0 when |z...

    Text Solution

    |

  18. Locate the region in the Argand plane for the complex number z satisfy...

    Text Solution

    |

  19. Indicate the region represented by pi/6leargzlepi/4 .

    Text Solution

    |

  20. Indicate the region in the Argand plane respresented by |z+1|^2+|z-1|^...

    Text Solution

    |