Supporting details are exemplified as the details like evidence in the form of facts or reason or the use of quotations or statistics that would function to act as a support to back the central idea or claim of the author and enhance the credibility of the claim.
The authors employ these details to 'strengthen their ideas and opinions' and convey them with more efficacy and clarity. These details may include the facts, comparison, statistics or quotation that would serve to enhance the validity of the author/speaker's claim or idea and make it more illustrative and clear for the audience to accept, believe, and elicit the desired response.
"Complex" is used here to describe the group of apartments. So, it qualifies for describing a noun, like the definition of adjective. Let me know if you got it right.
