The locus of the complex number z such that ( z-2 z+2 )= 3

Step-by-step solution

Let z=x+i y ( z-2 z+2 )= 3 aligned & (z-2)- (z+2)= 3 & ((x-2)+i y)- ((x+2)+i y)= 3 & ⁻¹ ( y x-2 )- ⁻¹ ( y x+2 )= 3 aligned array ll & ⁻¹ [ y x-2 - y x+2 1+ y x-2 y x+2 ]= 3 & [ 4 y x^2-4+y^2 ]= 3 = 3 array array ll & x^2-4+y^2= 4 y 3 & x^2+y^2- 4 y 3 -4=0 array Hence, it represents a equation of circle.