Home
Class 11
MATHS
P(z) be a variable point in the Argand p...

P(z) be a variable point in the Argand plane such that `|z|`=minimum `{|z−1, |z+1|}` , then `z+barz` will be equal to a. -1 or 1                                    b. 1 but not equal to-1 c. -1 but not equal to 1              d. none of these

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

If |z-3|=min{|z-1|,|z-5|} , then Re(z) equals to

If |z-1|=1, where z is a point on the argand plane, show that (z-2)/(z)=i tan (argz),where i=sqrt(-1).

If A(z_(1)) and B(z_(2)) are two points in the Argand plane such that z_(1)^(2)+z_(2)^(2)+z_(1)z_(2)=0 , then triangleOAB , is

Let z be a complex number satisfying |z-5i|<=1 such that amp(z) is minimum, then z is equal to

The locus of the point z is the Argand plane for which |z +1|^(2) + |z-1|^(2)= 4 is a

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 P (z) is a variable point in the complex plane such that IM (-1/z)=1/4 , then the value of the perimeter of the locus of P (z) is (use pi=3.14 )

If A(z_(1)),B(z_(2)) and C(z_(3)) are three points in the Argand plane such that z_(1)+omegaz_(2)+omega^(2)z_(3)=0 , then

If z=((1+i)/(1-i)), then z^4 equals to

lf z(!=-1) is a complex number such that [z-1]/[z+1] is purely imaginary, then |z| is equal to

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. If the equation whose roots are the squares of the roots of the cubic ...

    Text Solution

    |

  2. If sqrt(3)+i=(a+i b)(c+i d) , then find the value of tan^(-1)(b//a)+ta...

    Text Solution

    |

  3. P(z) be a variable point in the Argand plane such that |z|=minimum {|z...

    Text Solution

    |

  4. If the equation a x^2+b x+c=0,a ,b ,c , in R have none-real roots, t...

    Text Solution

    |

  5. Prove that the equation Z^3+i Z-1=0 has no real roots.

    Text Solution

    |

  6. The locus of point z satisfying R e(1/z)=k , where k is a non zero re...

    Text Solution

    |

  7. If p(q-r)x^2+q(r-p)x+r(p-q)=0 has equal roots, then prove that 2/q=1/p...

    Text Solution

    |

  8. Find the square root 9+40 idot

    Text Solution

    |

  9. Let alpha,beta in Rdot If alpha,beta^2 are the roots of quadratic e...

    Text Solution

    |

  10. Let a be a complex number such that |a|<1a n dz1, z2,z3,... be the ve...

    Text Solution

    |

  11. Let lambda in R . If the origin and the non-real roots of 2z^2+2z+lam...

    Text Solution

    |

  12. If the ratio of the roots of the equation x^2+p x+q=0 are equal to rat...

    Text Solution

    |

  13. Let z=1-t+isqrt(t^2+t+2), where t is a real parameter.the locus of the...

    Text Solution

    |

  14. If sintheta,costheta be the roots of a x^2+b x+c=0 , then prove that b...

    Text Solution

    |

  15. Express the following complex numbers in a+i b form: ((3-2i)(2+3i))/((...

    Text Solution

    |

  16. If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely i...

    Text Solution

    |

  17. If z^2+z|z|+|z^2|=0, then the locus z is a. a circle b. a straight ...

    Text Solution

    |

  18. If the sum of the roots of the equation 1/(x+a)+1/(x+b)=1//c is zero,...

    Text Solution

    |

  19. Solve the equation x^2+p x+45=0. it is given that the squared differen...

    Text Solution

    |

  20. Find the least positive integer n such that ((2i)/(1+i))^n is a positi...

    Text Solution

    |