A complementary infinitive is a use of the infinitive to complete the meaning of a verb. They usually occur with certain verbs.
I am able to finish this paper.
I desire to marry this girl.
I began to work on the project.
The above infinitive phrases are called “complementary” because they are the complement of the main verb of the sentence.
The infinitive will be anarthrous. cf. BBG 32.14; GGBB p. 598. The primary clue is the verb it completes. The following verbs often take complementary infinitives:
δυναμαι (always takes a complementary infinitive),
What was said above also applies to Hebrew. Hebrew infinitives are often complementary after the same verbs as listed above.