Question

A number of complaints have been received recently or has been received??

Answer 1

A number of complaints have been received recently

Answer 2

Use "have" because "complaints" is plural. It it were just one complaint, it would be has.

Answer 3

Ignore the prepositional phrase that intervenes between the subject and verb. The object of that phrase cannot also be the subject of the sentence.

Here's a link with lots of great info on s/v agreement --

http://www.towson.edu/ows/moduleSVAGR.htm