Question

If | z2 - 1 | = | z |2 + 1, then z lies on

Answer 1

2z+1=z*3
2z+1=3z
3z-2z=1
z=1

Answer 2

Let $\;z=x+iy$

Then , $\;|z^{2}-1| = |z|^{2}+1\;$

$|x^{2}-y^{2}-1+i2xy | = |x+iy|^{2}+1$

$(x^{2}-y^{2}-1)^{2}+4x^{2}y^{2} =(x^{2}+y^{2}+1)^{2}$

$4x^{2}=0\;$ i.e x=0

Hence z lies on y-axis