Inverse Points with Respect to a Circle

Q. Let $z=1-t+i\sqrt{t^2+t+2}$, where $t$ is a real parameter. The locus of $z$ in Argand plane is

1. a hyperbola
2. an ellipse
3. a straight line
4. a circle

Q. Let $z=1-t+i\sqrt{t^2+t+2}$, where $t$ is a real parameter. The locus of $z$ in Argand plane is

1. a hyperbola
2. an ellipse
3. a straight line
4. a circle