Answer
All the points that lie outside the sphere with center (0, 0, 1) and radius 1.
Work Step by Step
We first rewrite the inequality so that it resembles the form for a sphere. We do this by completing the square as follows:
$x^{2} + y^{2} + z^{2} \gt 2z$
$x^{2} + y^{2} + z^{2} - 2z \gt 0$
$x^{2} + y^{2} + z^{2} - 2z + 1 \gt 1$
$x^{2} + y^{2} + (z - 1)^{2} \gt 1$
Now we can see that the inequality represents all the spheres centered at (0, 0, 1) with a radius greater than $\sqrt 1$ = $1$. Such spheres will occupy the entire three-dimensional space with the exception of the points that lie inside the sphere with radius 1 and center (0, 0, 1)
