Act IV is essential for us to understand Iago's persuasive power, the level of his envy, and Othello's insecurity and inconsequence.
In this case, we can see that in act IV, Othello shows himself as a bad husband, because in addition to not believing in his wife, whom he swore to love and trust, he prefers to give reason to someone with whom he has no responsibility or intimacy, Iago, who on top of everything else is lying.
Desdemona's death in Act V is not a relief for the way she is being treated, on the contrary, Desdemona's death is the culmination of cruelty towards her, Othello's inconsequence, and Iago's persuasion.
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