A complementary infinitive is a use of the infinitive to complete the meaning of a verb. They usually occur with certain verbs.
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. In the following example, the infinitive construct is expressing the complementary action of the main verb.
|וָאֵרֵ֞ד לְהַצִּיל֣וֹ מִיַּ֣ד מִצְרַ֗יִם וּֽלְהַעֲלֹתוֹ֮ מִן־הָאָ֣רֶץ הַהִוא֒
|I have come down to free them from the Egyptians’ power and to bring them up from that land
|הִנֵּ֥ה הָעָ֛ם חֹטִ֥אים לַֽיהוָ֖ה לֶאֱכֹ֣ל עַל־הַדָּ֑ם
|Look, the people are sinning against Yahweh by eating with the blood.