(%i347) declare(x,complex)$
(%i348) [conjugate(x) - x = 0, sqrt(-x^2-1) - conjugate(sqrt(-x^2-1))=0]$
Wrong---the solution set is empty
(%i349) %solve(%,x);
(%o349) %union([x=%c1191])
See also https://groups.google.com/group/sage-support/browse_thread/thread/a105bcce5be83ee?hl=en