If a complex number z satisfies |z|^2+1= z^2-1 , then the locus of z is

Step-by-step solution

aligned & Let z=x+i y , so & |z|^2+1= |z^2-1 | aligned aligned & x^2+y^2+1= (x^2-y^2-1 )^2+4 x^2 y^2 & (x^2+y^2+1 )^2= (x^2-y^2-1 )^2+4 x^2 y^2 & (x^2+y^2+1 )^2- (x^2-y^2-1 )^2=4 x^2 y^2 & [ (x^2+y^2+1 )+ (x^2-y^2-1 ) ] & [ (x^2+y^2+1 )- (x^2-y^2-1 ) ]=4 x^2 y^2 & (2 x^2 ) (2 y^2+2 )=4 x^2 y^2 & x^2 y^2+2 x^2=x^2 y^2 x^2=0 x=0, aligned so locus is a imaginary axis.