A complementary infinitive is a use of the infinitive to complete the meaning of a verb. They usually occur with certain verbs.
The above infinitive phrases are called “complementary” because they are the complement of the main verb of the sentence.
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Greek:
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:
αρχομαι,
βουλομαι,
δυναμαι (always takes a complementary infinitive),
επιτρεπω,
ζητεω,
θελω,
μελλω,
οφειλω.
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Hebrew:
What was said above also applies to Hebrew. Hebrew infinitives are often complementary after the same verbs as listed above.