use complex analysis to factor the following polynomials into a product of two quadratic polynomials:

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sketch :

and determine if the set is :

open,closed,bounded,connected ,simply connected , domain,compact or region

answer :

the given set is :

closed,connected ,simply connected ,and region

but not :

open,bounded,domain,and compact

my question : if the question : arg z not Arg z"principle argument" the answer is the same or not ???