Home
Class 11
MATHS
If the roots of (z-1)^n=i(z+1)^n are plo...

If the roots of `(z-1)^n=i(z+1)^n` are plotted in ten Arg and plane, then prove that they are collinear.

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 point 'z' is equidistant from three distinct points z_(1),z_(2) and z_(3) in the Argand plane. If z,z_(1) and z_(2) are collinear, then arg (z(z_(3)-z_(1))/(z_(3)-z_(2))). Will be (z_(1),z_(2),z_(3)) are in anticlockwise sense).

if omega is the nth root of unity and Z_1 , Z_2 are any two complex numbers , then prove that . Sigma_(k=0)^(n-1)| z_1+ omega^k z_2|^2=n{|z_1|^2+|z_2|^2} where n in N

If n >1 , show that the roots of the equation z^n=(z+1)^n are collinear.

Show that the roots of equation (1+z)^n=(1-z)^n are -i tan (rpi/n), r=0,1,2,,…………,(n-1) excluding the vlaue when n is even and r=n/2

Find the locus of z if arg ((z-1)/(z+1))= pi/4

If z_1, z_2, z_3 are three nonzero complex numbers such that z_3=(1-lambda)z_1+lambdaz_2 w h e r e lambda in R-{0}, then prove that points corresponding to z_1, z_2a n dz_3 are collinear .

If arg z = alpha and given that |z-1|=1, where z is a point on the argand plane , show that |(z-2)/z| = |tan alpha |,

If z_(1),z_(2),z_(3),…,z_(n-1) are the roots of the equation z^(n-1)+z^(n-2)+z^(n-3)+…+z+1=0 , where n in N, n gt 2 and omega is the cube root of unity, then

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

If 1,z_1,z_2,z_3,.......,z_(n-1) be the n, nth roots of unity and omega be a non-real complex cube root of unity, then prod _(r=1)^(n-1) (omega-z_r) can be equal to

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If nge3and1,alpha(1),alpha(2),alpha(3),...,alpha(n-1) are the n,nth ...

    Text Solution

    |

  2. How many roots of the equation 3x^4+6x^3+x^2+6x+3=0 are real ?

    Text Solution

    |

  3. If the roots of (z-1)^n=i(z+1)^n are plotted in ten Arg and plane, the...

    Text Solution

    |

  4. Find the value of k if x^3-3x+k=0 has three real distinct roots.

    Text Solution

    |

  5. Let z=t^2-1+sqrt(t^4-t^2),where t in R is a parameter. Find the locu...

    Text Solution

    |

  6. If|z|=1 , then prove that points represented by sqrt((1+z)//(1-z)) lie...

    Text Solution

    |

  7. If omega is an imaginary fifth root of unity, then find the value of ...

    Text Solution

    |

  8. a ,b ,a n d c are all different and non-zero real numbers on arithmet...

    Text Solution

    |

  9. Let x^2+y^2+x y+1geqa(x+y)AAx ,y in R , then the number of possible i...

    Text Solution

    |

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

    Text Solution

    |

  11. If w=alpha+ibeta, where beta!=0 and z!=1 , satisfies the condition tha...

    Text Solution

    |

  12. If z is a non real root of root(7)(-1) , then find the value of z^(86...

    Text Solution

    |

  13. The quadratic equation x^2+m x+n=0 has roots which are twice those of ...

    Text Solution

    |

  14. Let omega=-1/2+i(sqrt(3))/2, then value of the determinant [[1, 1, 1]...

    Text Solution

    |

  15. All the value of k for which the quadratic polynomial f(x)=2x^2+k x+2=...

    Text Solution

    |

  16. If a=cos(2pi//7)+isin(2pi//7), then find the quadratic equation whose ...

    Text Solution

    |

  17. Let complex numbers alpha and 1/alpha lies on circle (x-x0)^2+(y-y0)^2...

    Text Solution

    |

  18. If |z/| barz |- barz |=1+|z|, then prove that z is a purely imaginary ...

    Text Solution

    |

  19. If x=-5+2sqrt(-4) , find the value of x^4+9x^3+35 x^2-x+4.

    Text Solution

    |

  20. Let a , b ,a n dc be rel numbers which satisfy the equation a+1/(b c)=...

    Text Solution

    |