After I finish my homework I will listen to the radio. Is this sentence a complex sentence?

Yes.

To determine whether a sentence is a complex sentence, you need to first understand the structure of a complex sentence.

A complex sentence consists of an independent clause and one or more dependent clauses. An independent clause can stand alone as a complete sentence, while a dependent clause cannot. In your sentence, "After I finish my homework" is a dependent clause, and "I will listen to the radio" is an independent clause.

To identify the independent and dependent clauses, you can break down the sentence:

1. "After I finish my homework" - This is the dependent clause because it does not express a complete thought on its own. It depends on the independent clause to provide the full meaning.

2. "I will listen to the radio" - This is the independent clause because it expresses a complete thought and can stand alone as a sentence.

Based on this analysis, the given sentence "After I finish my homework I will listen to the radio" is indeed a complex sentence.