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### 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 < (2I), (4I + 4)z + 7 > 0], [z == (2I), (8I - 1) > 0], [(2I) < z, (4I + 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?

 2 None vdelecroix 7397 ●19 ●81 ●164 http://www.labri.fr/pe...

### 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:  inequation:

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