In the complex plane C , the set z C: ( z-1 z+1 )= 4 represents

Step-by-step solution

Let a complex number z=x+i y , then aligned z-1 z+1 & = (x-1)+i y (x+1)+i y (x+1)-i y (x+1)-i y & = (x^2+y^2-1 )+i y(x+1-x+1) (x+1)^2+y^2 & = (x^2+y^2-1 ) (x+1)^2+y^2 +i 2 y (x+1)^2+y^2 aligned According to the given information, gathered ( z-1 z+1 )= 4 2 y (x^2+y^2-1 ) =1 x^2+y^2-2 y-1=0 gathered The complex plane C represents a circle. Hence, option (b) is correct.