Home
Class 11
MATHS
if iz^3+z^2-z+i=0 then show that absz=1...

if `iz^3+z^2-z+i=0` then show that `absz=1`

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos
  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

If iz^3+z^2-z+i=0 then the value of abs(z) is

If |z_(1)|=|z_(2)|=1 and argz_(1)+argz_(2)=0 then show that z_(1)=1

If x+y+z=0 then show that abs((1,1,1),(x,y,z),(x^3,y^3,z^3)) = 0.

If 8iz^3+12z^2-18z+27i=0, then (a). |z|=3/2 (b). |z|=2/3 (c). |z|=1 (d). |z|=3/4

If z_1, z_2, z_3 are three complex numbers such that 5z_1-13 z_2+8z_3=0, then prove that [(z_1,(bar z )_1, 1),(z_2,(bar z )_2 ,1),(z_3,(bar z )_3 ,1)]=0

If |z_(1)|=|z_(2)|and argz_(1)+argz_(2)=0, then show that z_(1) and z_(2) are tow complex conjugate numbers. '

If z=x+iy and |z-1|+|z+1|=4,then show that 3x^2+4y^2=12 ,where i=sqrt-1

if x+y+z=0 , then show that, |{:(1,1,1),(x,y,z),(x^3,y^3,z^3):}|=0

If z be a complex number satisfying z^4+z^3+2z^2+z+1=0 then absz is equal to

If z=x+iyandw=(1-iz)/(z-i) such that |w|=1 , then show that z is purely real.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Intercept made by the circle zbar z +bar az+abar z+r=0 on the real a...

    Text Solution

    |

  2. The graph of the quadratic trinomial y=a x^2+b x+c has its vertex at (...

    Text Solution

    |

  3. if iz^3+z^2-z+i=0 then show that absz=1

    Text Solution

    |

  4. Show that the equation of a circle passing through the origin and ha...

    Text Solution

    |

  5. The function f(x)=a x^3+b x^2+c x+d has three positive roots. If the ...

    Text Solution

    |

  6. let z1=10+6i and z2=4+6i if z is nay complex number such that argument...

    Text Solution

    |

  7. Let vertices of an acute-angled triangle are A(z1),B(z2),a n dC(z3)dot...

    Text Solution

    |

  8. If (18x^2+12x+4)^n = a0 +a(1x)+ a(2x)^2 +......+ a(2n)x^(2n), prove th...

    Text Solution

    |

  9. If z=z0+A( bar z -( bar z 0)), w h e r eA is a constant, then prove t...

    Text Solution

    |

  10. If (sinalpha)x^2-2x+bgeq2 for all real values of xlt=1a n dalpha in (0...

    Text Solution

    |

  11. If z1, z2, z3 are three complex numbers such that 5z1-13 z2+8z3=0, t...

    Text Solution

    |

  12. If one root x^2-x-k=0 is square of the other, then k= a.2+-sqrt(5)...

    Text Solution

    |

  13. If z1, z2 are complex number such that (2z1)/(3z2) is purely imaginary...

    Text Solution

    |

  14. If alpha,a n dbeta be the roots of the equation x^2+p x-1//2p^2=0,w h ...

    Text Solution

    |

  15. If z1,z2,z3 are complex numbers such that 2/z1=1/z2 + 1/z3, show that ...

    Text Solution

    |

  16. Find the range of f(x)(x^2-x+1)/(x^2+x+1)

    Text Solution

    |

  17. If ((3-z1)/(2-z1))((2-z2)/(3-z2))=k(k >0) , then prove that points A(z...

    Text Solution

    |

  18. x^2-x y+y^2-4x-4y+16=0 represents a. a point b. a circle c. ...

    Text Solution

    |

  19. If (x+i y)^5=p+i q , then prove that (y+i x)^5=q+i pdot

    Text Solution

    |

  20. If alpha,beta are the nonzero roots of a x^2+b x+c=0 and alpha^2,beta^...

    Text Solution

    |