The equation a r g z - 1 z + 1 = π 4 represents a circle with:

The equation argz-1z+1=π4 represents a circle with:
  1. centre at (0,0) and radius 2
  2. centre at (0,1) and radius 2
  3. centre at (0,-1) and radius 2
  4. centre at (0,1) and radius 2

Solution

We have,

argz-1z+1=π4

argz0-1z0+1=π2

⇒z0-1z0+1=eiπ2

⇒z0-1z0+1=i

⇒z0=1+i1-i

⇒z0=(1+i)22

⇒z0=i

⇒ Centre 0,1

Radius is the distance between z0 and -1,0

=-1-02+0-12

=2 units

Asked in: JEE Main 2021 (26 Aug Shift 1)

Practice more Complex Number questions on Aicharya