# Plot all complex numbers, for which a predicate holds

How do I solve the following exercise in SageMath?

Outline (in the complex number plane) all numbers z in ℂ, for which `abs(z+2)^2 > abs(z-2*I)^2+1`

holds.

So, I figured the first step is to actually solve the inequation:

```
sage: sol=solve(abs(z+2)^2 > abs(z-2*I)^2+1, z) #0: solve_rat_ineq(ineq=(_SAGE_VAR_z+2)^2 > abs(_SAGE_VAR_z-2*%i)^2+1)
sage: sol
[[z < (2*I), (4*I + 4)*z + 7 > 0],
[z == (2*I), (8*I - 1) > 0],
[(2*I) < z, (4*I + 4)*z + 7 > 0]]
```

Okay, first, how do I interpret this solution? Every element in the list is a list of terms that must all hold? And of course, how can I now plot all those solutions?

It seems that teaching SageMath to do $|x+iy|^2=x^2+y^2$ is harder than doing it by hand.