Τελειόω Contract Verb

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Sorry if this is a stupid question, but I am having confusion over this type of contract verb: τελειόω. Do I start with the ει and contract it with the omicron and then contract that with the ending. Or do I still start with the omicron and contract the omicron with the ending?

The latter. τελειόω behaves like any -όω contract verb, e.g. δηλόω. So the -όω contracts to -ῶ, etc., and the τελει- part is not affected. So aor. ἐτελείωσα, etc.etc. The only complication with this particular verb is that τελει- is often spelled τελε-, just as the adjective is often τέλεος rather than τέλειος.

τελε-όω (>τελε-ῶ) is not to be confused with τελέ-ω (>τελῶ), a related and much commoner verb.

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Thank you. I have seen the example with δηλόω but it threw a curve at me when the omicron was proceeded by a vowel, a diphthong in this case. Plus the rest of the information is very valuable.