They expect to be invited
Here, this sentence is a passive voice. What is the active voice of it. If it haven't then give reasons please.
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The sentence you give is in the active voice.
The passive version of the sentence could be something like:
An invitation is expected.
If you're actually talking about the passive infinitive of to be invited then a similar change could be made to the original sentence:
They expect an invitation.
Or, to assume more about the context and keep the second verb:
They expect their friends will invite them.