Home
Class 11
MATHS
Let z1=10+6i and z2=4+6idot If z is any ...

Let `z_1=10+6i` and `z_2=4+6idot` If `z` is any complex number such that the argument of `((z-z_1))/((z-z_2))` is `pi/4,` then prove that `|z-7-9i|=3sqrt(2)` .

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

Let z_1=6+i and z_2=4-3i . If z is a complex number such thar arg ((z-z_1)/(z_2-z))= pi/2 then (A) |z-(5-i)=sqrt(5) (B) |z-(5+i)=sqrt(5) (C) |z-(5-i)|=5 (D) |z-(5+i)|=5

If z_1=i z_2 and z_1-z_3=i(z_3-z_2) ,then prove that |z_3|=sqrt(2)|z_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

If z_1=10+6i and z_2=4+2i be two complex numbers and z be a complex number such that a r g((z-z_1)/(z-z_2))=pi/4 , then locus of z is an arc of a circle whose (a) centre is 5+7i (b) centre is 7+5i (c) radius is sqrt(26) (d) radius is sqrt(13)

If z be any complex number (z!=0) then arg((z-i)/(z+i))=pi/2 represents the curve

Let z!=i be any complex number such that (z-i)/(z+i) is a purely imaginary number. Then z+ 1/z is

For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

For any complex number z prove that |R e(z)|+|I m(z)|<=sqrt(2)|z|

Let z be a complex number such that |z|+z=3+I (Where i=sqrt(-1)) Then ,|z| is equal to

Let z_(1),z_(2) and z_(3) be three complex number such that |z_(1)-1|= |z_(2) - 1| = |z_(3) -1| and arg ((z_(3) - z_(1))/(z_(2) -z_(1))) = (pi)/(6) then prove that z_(2)^(3) + z_(3)^(3) + 1 = z_(2) + z_(3) + z_(2)z_(3) .

CENGAGE ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. Show that the equation of a circle passing through the origin and ha...

    Text Solution

    |

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

    Text Solution

    |

  3. Let z1=10+6i and z2=4+6idot If z is any complex number such that the a...

    Text Solution

    |

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

    Text Solution

    |

  5. If (18 x^2+12 x+4)^n=a0+a(1x)+a2x2++a(2n)x^(2n), prove that ar=2^n3^r(...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  10. If 2z1//3z2 is a purely imaginary number, then find the value of "|"(z...

    Text Solution

    |

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

    Text Solution

    |

  12. If z1, z2, z3 are complex numbers such that (2//z1)=(1//z2)+(1//z3), t...

    Text Solution

    |

  13. Find the range of (a) f(x) = (x^(2)+34 x - 71)/(x^(2) + 2x - 7) (b...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. Find real value of theta for which (3+2i sin theta)/(1-2i sin theta) i...

    Text Solution

    |

  19. If the roots of the equation a x^2+b x+c=0 are of the form (k+1)//ka n...

    Text Solution

    |

  20. Prove that tan(iloge((a-ib)/(a+ib)))=(2ab)/(a^2-b^2) (where a, b in ...

    Text Solution

    |