Let z₁, z₂, z₃ be three vertices of an equilateral triangle circumscribing the circle |z|= 1 2 . If z₁= 1 2 + i 3 2 and z₁, z₂ , z₃ were in anticlockwise sense, then z₂ is

Step-by-step solution

Given that, |z|= 1 2 and z₁= 1 2 + 3 i 2 Here, one of the number must be a conjugate of z₁= 1 2 + 3 i 2 i.e. z₂= 1 2 - 3 i 2 and z₂=z₁ e^ -i 2 / 3 aligned z₂ & = ( 1 2 + i 3 2 ) [ 2 3 +i 2 3 ] & =-2 1 2 =-1 & [ (1+i 3 ) ( 2 3 +i 2 3 )=-2 ] aligned