Give examples of Iago's two-faced behaviour. How might an actor convey this?

A major "two-faced behavior" that Iago has is his jealousy
for Othello, believed to be from a deep sexual connection he feels he shares with
Othello. He plots against Othello, while deeply longing for his love. He consequently
lies to himself and acts out of this internal
struggle. 

The dream sequence in Act III Scene III where
Iago is describing a dream that Cassio had about Desdemona is dripping with sexuality
and showcases the sexual nature of male relationships in the time of the play. Iago says
that Cassio "kiss [him] hard" and climbed on top of him, kissing him repeatedly and
moaning. Othello upon hearing this homoerotic tale does not question why Cassio and Iago
were in bed together, why Iago didn't wake him up after the first kiss, or anything or
the nature. The fact Iago freely talks about sleeping with Cassio and it is not a big
deal, nor does Othello act surprised to hear this or question what they were doing
together, illustrates that men had sexual relationships that were more than acceptable,
but common. 

So, within Iago, his motives are not
explicitly stated, but his jealousy for Othello is apparent and the reader is meant to
question why? I argue that it is all from the fact Iago wants the love Othello gives
Desdemona, and when he cannot receive it (and possibly assumes he never will), allows
his jealousy to blind him and sweep him into a plot with no turning
back.

An actor lucky enough to play Iago should relish in
the implicit sexuality the character carries himself with throughout the play. Deciding
how to express this sexual frustration, through body language or adopted word play that
emphasized his burden of love (inflections of tone when talking to Othello, showing
disdain for Desdemona), and show the audience that unlike today, homosocial relations
were also often homoerotic. Expressing Iago through his most primal, animalistic
emotions of hunger and sexual desire for Othello would surely show internal conflict,
where he disguises the truth from the world, keeping his mask on and the truth
hidden.