To identify the total number of complaints for a given delivery by domain, the "Non-deliverables and bounces" report would be appropriate. This report typically includes data on email delivery issues, which encompass bounces, spam complaints, and other non-delivery related events categorized by domain.
Complaints are a form of non-deliverable where the recipient's email server has accepted the email but classified it as spam or junk, often feeding back to the sending server as a complaint.References:This functionality is part of Adobe Campaign Classic's reporting capabilities, providing insight into the deliverability issues including complaints by domain.