A complex clause is a °clause that contains at least one other °clause.
The term "complex sentence" is often used as an alternative (but less precise) term.
complex sentence (CXN) = a construction made up of more than one clausal construction. Example: [The birds were singing] [when I went out to get the newspaper] is an instance of a complex sentence construction consisting of two clauses, indicated by square brackets in the example. (Sections 1.3, 15.1.1)