In act 1, scene 1 of Othello, what are Roderigo's and Iago's feelings toward Othello?

Othello is the tragic story of how miscommunication changes lives. The audience is introduced to Othello through the words of Iago and Roderigo in Act I, scene i with Othello only making his entrance in scene ii. It is possible, and apparently purposeful on Shakespeare's part, that if Iago is to be believed, Othello is  a person who "loving his own pride and purposes" (12) has made an inappropriate choice for his lieutenant, and unfairly passed over the most-deserving candidate (who is of course Iago) from "whom his eyes had seen the proof" (28). The audience is even possibly inclined to feel the same way as Iago, and this is encouraged by Roderigo's part as he too feels that Iago is justified to "hold him (Othello) in thy hate" (7). Roderigo is so enraged by Othello's apparent poor choices and is already falling into Iago's trap. He too would despise Othello if his reward for success in battle was to be nothing more than to be Othello's "ancient" (33). 

Iago admits that he will take the first opportunity "to serve my turn upon him" (42). Iago also knows that Roderigo has his own reasons for disliking Othello and that Roderigo relishes any chance to get closer to Desdemona. He acts and speaks before he thinks and Iago intends to make use of this characteristic to further his own aims. Roderigo knows that Brabantio (Desdemona's father) has turned him away before, for being unsuitable for Desdemona, but he is so inspired by Iago's talk of revenge against Othello, that he demeans himself, "a knave of common hire" (126) so that he can reveal Othello as even worse- "a lascivious Moor" (127) and so help Iago destroy Othello's reputation and standing, such is the level of his self-absorption. He does not realize that his words do not make him a better candidate for Desdemona's attentions. It becomes obvious, therefore that both men despise Othello for their circumstances rather than looking at their own shortcomings. 

What is the relationship between Iago and Roderigo in Othello?

One is a puppet master; the other, a puppet. Iago plays Roderigo like a puppet. He uses him and his money for his own ends, chief of which is to harm Othello. Othello has supposedly humiliated Iago by appointing an inexperienced foreigner, Cassio, as his lieutenant and ignoring him in spite of the fact that he has been his loyal, brave, and experienced servant, and Iago seeks vengeance for this.

From the outset, Iago has no qualms about using the foolish and gullible Roderigo, who virtually becomes the deceitful and sly manipulator's slave. He does Iago's bidding at a whim, without much question as he did when, in Scene 1 of Act I, he was instructed to deceive Brabantio into believing that Othello had abducted his daughter and was in the process of abusing her.

Furthermore, Iago is in control of Roderigo's seemingly ample purse and consistently asks him for money and Roderigo, like a dunce, willingly complies to his requests. The sole reason for all his acquiescence is that Iago is dangling the fact that he will help the besotted dolt win Desdemona's affection like a carrot in front of him. Roderigo is obsessed with the beautiful Desdemona, Othello's wife, and would do everything to have her.

Iago remorselessly uses this promise to exploit Roderigo and he declares, at various stages in the play, what he thinks of Roderigo and why he is playing him for a fool. For example, at the end of Act I, Scene 3:

Thus do I ever make my fool my purse:
For I mine own gain'd knowledge should profane,
If I would time expend with such a snipe.
But for my sport and profit.

In these lines, Iago most pertinently states that he would not have spent time with such a foolish person if it were not for his own "sport and profit." It is clear that he does not see Roderigo as a friend but rather as a tool that he can use for his own pleasure and benefit. The fact that he refers to Roderigo as a "fool" whom he makes his "purse" further emphasizes the fact that he is shamelessly using him.

Roderigo, however, seems to believe Iago actually has the power to ensure him success in getting Desdemona's attention and winning her over. He believes Iago is his friend, consistently follows his advice, and is even prepared to disguise himself and undertake an arduous sea journey to a dangerous place just to be close to Desdemona and improve his lot. One can only pity such a gullible sacrifice. When Roderigo eventually realizes that he has been mislead by empty promises, most of the damage has already been done and he has lost practically his entire wealth to Iago.

In this regard, then, Roderigo's confrontation with Iago is a sad failure because he is once again persuaded by the glib and masterful schemer that all is going well and that whatever he, Roderigo, may believe, is a figment of his imagination. So persuasive is Iago that Roderigo, once again, does his bidding and goes out of his way in trying to kill Cassio as instructed.

In the end, Roderigo pays a terrible price for his subservience and his ignorance. Not only does he lose his material wealth and his chance at love, but he also loses his life at the hands of the one he trusted the most, Iago. It is ironic that his intention to expose his malicious master only becomes evident after his own death.

What is the relationship between Iago and Roderigo in Othello?

In Othello, Shakespeare begins the play with two foils, Iago and Roderigo at night: one hidden and the other in plain sight.  The former is a villain, the latter a fool, but both are be dark lords of misrule.

Here's what they have in common:

• Both are targeting Desdemona (Roderigo as thwarted love; Iago as revenge bait against Othello)
• Both are jealous of Othello
• Both are expose Desdemona's secret elopement to Brabantio (Roderigo publicly; Iago privately)
• Both lose their battle against Othello in Act I (the Duke condones the marriage)
• Both seek revenge in Cyprus (away from the Duke's protection)
• Both are id-based characters (exhibit child-like behavior and seek immediate pleasure: Roderigo=lust; Iago=suffering of others)

Here's how they are different:

• Roderigo is public in Venice and private in Cyprus; Iago is private in Venice and public and private in Cyprus: (as such, they are two halves of the hidden, dark side).
• Roderigo is pure passion (he threatens suicide); Iago is calculated passion (he wants only to wound others)
• Roderigo pays Iago.  Roderigo is the "money" and Iago is the "purse."
• Roderigo is a fool.  Iago admits, "I am not what I am" to Roderigo, and yet Roderigo continues to believe and pay him
• Roderigo thinks his using Iago for his dirty work, but Iago is really using Roderigo to be his scapegoat.  Iago uses Rogerigo to expose Cassio.

In Othello, what are Roderigo's and Iago's feelings towards Othello?

Iago and Roderigo both despise Othello but it is Iago who has an irrational desire to ruin Othello. Roderigo's hatred is based on Roderigo's own apparent 'love' for Desdemona. He is so foolish that he thinks that Desdemona can be his if only Othello is out of the picture.

Roderigo is Iago's pawn, doing his bidding and even paying Iago to secure his favor with Desdemona. He allows Iago to manipulate him and even when he realizes that Iago has only his own interests at heart, "I do not find that thou deal'st justly with me"  and he has "wasted myself out of my means"  he is still persuaded to act to secure his love interest.

The hatred Iago has for Othello is immeasurable and, in some instances, unfounded. He is paranoid and believes Othello may have even

  leap'd into my seat; the thought whereof
Doth (like a poisonous mineral) gnaw my inwards

He has no reason to think this and even Emilia tells him it's absurd.

The fact that Cassio was promoted sets Iago off on his path to destroy Othello as he cannot believe that there is any sensible reason why Cassio would have been promoted over him, an experienced soldier.

Revenge is the main motivator for Iago and all his actions come together so that it appears that he is not the only instigator, having most of his compatriots believing he is "honest" Iago.

It is perhaps the similarities between Iago and Othello that push Iago to destroy Othello and all those connected to him

Iago is the only character who speaks directly to Othello's sense of his own inadequacy.

Iago almost relishes his devilment, "I am a very villain else" and his feelings towards Othello do not falter. Each occurrence serves to strengthen his resolve and with Roderigo as his willing co-conspiritor, he cannot be stopped.