Home
Class 12
MATHS
The center of the arc represented by ar...

The center of the arc represented by ` arg[(z-3i)/(z-2i + 4)] = pi/4`

Text Solution

Verified by Experts

If C is the centre of the arc, then `/_BCA = pi//2`

Let C be `z_(c)`. Then,
`(z_(c) - 3i)/(z_(c) - 2i + 4) = e^(ipi//2=i)`
`z_(c) = 3i + i(z_(c) - 2i + 4)`
`therefore z_(c)= (7i + 2)/((1-i))= (1)/(2) (9i - 5)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.11|6 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise (Single)|89 Videos

  • COMPLEX NUMBERS

    CENGAGE|Exercise Exercise 3.9|8 Videos

  • CIRCLES

    CENGAGE|Exercise Question Bank|32 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|91 Videos

Similar Questions

Explore conceptually related problems

Find the center of the are represented by arg[(z-3i)/(z-2i+4)]=pi/4

Perimeter of the locus represented by arg((z+i)/(z-i))=(pi)/(4) equal to

The pointo fintersection of the cures represented by the equations art(z-3i)= (3pi)/4 and arg(2z+1-2i)= pi/4 (A) 3+2i (B) - 1/2+5i (C) 3/4+9/4i (D) none of these

The number of points of intersection of the curves represented by arg(z-2-7i)=cot^(-1)(2) and arg ((z-5i)/(z+2-i))=pm pi/2

If the locus of the complex number z given by arg(z+i)-arg(z-i)=(2pi)/(3) is an arc of a circle, then the length of the arc is

Plot the region represented by (pi)/(3)<=arg((z+1)/(z-1))<=(2 pi)/(3) in the Argand plane.

Find the point of intersection of the curves arg(z-3i)=(3 pi)/(4) and arg (2z+1-2i)=pi/4

Number of points of intersections of the curves Arg((z-1)/(z-3))=(pi)/(4) and Arg(z-2)=(3 pi)/(4) are

Number of points of intersections of the curves Arg((z-1)/(z-3))=(pi)/(4) and Arg(z-2)=(3 pi)/(4) are