<s>[INST] Plot $|z^2-1|=1$ $$|z^2-1|=1$$
$|x^2-y^2-1+2xyi|=1$
$\sqrt{(x^2-y^2-1)^2+(2yx)^2}=1$
${(x^2-y^2-1)^2+4x^2y^2}=1$
$x^4+y^4+2x^2y^2+2x^2-2y^2=1$
$(x^2+y^2)^2=2(x^2-y^2)+1$
I am trying to bring it to the form of $(x^2+y^2)^2=2a(x^2-y^2)$ but cant get rid of the $1$
 [/INST] Hint
$$(x^2-y^2-1)^2+4x^2y^2=1\to (x^2-y^2)^2-2(x^2-y^2)+1+4x^2y^2=1$$
$$(x^2+y^2)^2-2(x^2-y^2)=0\to (x^2)^2+x^2(2y^2-2)+y^4+2y^2=0$$
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