Why is Iago's suspicion that Othello and Cassio have slept with Emilia particularly significant?Is it to do with his insecurities? And does it create a complex character for Iago?
Iago has no good reason to suspect either Cassio or Othello of committing adultery with Emilia. She does not seem like a loose woman or an especially attractive women. Iago's motivation for plotting against Othello has been questioned for centuries. Iago seems capable of justifying his congenital villainy by rationalization. He could benefit by ruining Cassio, because he would automatically become Othello's lieutenant; but he would not benefit by undermining Othello, because he is dependent upon Othello for his job, and there is no way in which he could move up into Othello's position. Iago's motivation is never satisfactorily explained. Even at the end of the play, when he has been exposed as a demidevil, he refuses to explain why he practiced against Othello.
Will you, I pray, demand that demidevil
Why he hath thus ensnared my soul and body?
Demand me nothing. What you know, you know.
From this time forth I never will speak word.
(Act 5, Scene 2)
Even when his captors promise to use the worst kinds of torture to get the truth out of him, Iago refuses to explain his motives. Why shouldn't he defend himself as best he can? He can't because he doesn't have logical and plausible motives. If he brought out his "suspicions" of Emilia's adulterous relations with Cassio and Othello, they would all laugh at him. If he really suspects his wife, he should take his anger out on her. He obviously is quite capable of that.
Shakespeare struggled with Iago's motivation throughout the play. It is noteworthy that Iago says he suspects both Cassio and Othello of sleeping with Emilia. This makes his case look weaker, not stronger. It is impossible to believe that Othello would be interested in Emilia, and nearly as difficult to believe that Cassio would be interested in her. It is as if Iago cannot come up with sufficient reasons for hating both men and has to make one questionable suspicion do double duty.
Iago's suspicion "that Othello and Cassio have slept with Emilia" is only significant, in my opinion, because it shows the weakness in Iago's motivation.