According to the Ibn Ezra, Achashverosh was angry from the time he woke up from his drunken stupor after following Haman’s decree to rid himself of Vashti (Esther 2:1) until Haman was ultimately hanged.
The Me’am Loez explains the subsiding of the king’s fury as calm that returned to the universe.
This is because, as the Sfas Emes writes, when Amalek is in power, H-Shem is more noticeable through His characteristic of din, judgment. This is similar to what Rashi writes in his commentary on Torah (Shemos 17:16).
Haman’s end brought with it a sense of peace. The Talmud in several places (Rosh HaShanah 12a, Sanhedrin 108b, Zevachim 113b) points out that regarding the Flood, the verse (Bireishis 8:1) says “vayishku mayim” (“and the water subsided”) when the waters cooled down, whereas the phrase in this verse is “v’chamas hamelech shichacha” (“and the fury of the king subsided”). The contrast in phrasing implies that the flood waters were hot to match the burning passions of the licentious people of that time, mida kineged mida.
Parenthetically, perhaps another connection between the flood and Haman’s downfall is the Midrashic opinion (Yalkut Shimoni 6:1056) that Haman built the gallows from the beams of Noach’s ark.
Interestingly, shachacha (“subsided”) is a unique word in TaNaCh. R’ Samson Raphael Hirsch (Collected Writings, Volume IV, 319) comments that the word, shachach is phonetically related to shagag, (“not by choice”). In other words, the king’s anger was not something Achashverosh put effort into controlling. It came and subsided without any input from him.
The Talmud (Megillah 16a) considers that the unique spelling of shacha with an extra letter chuf to read shachacha is due to the fact that two angers were cooled; one belonged to the King of the Universe and the other belonged to Achashverosh. Also, Achashverosh calmed down about the situation of Esther, and the situation of Vashti.
As Rashi explains, Achashverosh was doubly angry because Haman was seemingly responsible for the death of Vashti, and was now a threat to Esther.
The Maharsha emphasizes that Achashverosh was still angry from that point (Esther 2:1), chronologically almost a decade earlier.
R’ Dovid Feinstein explains that Achashverosh had held himself responsible for Vashti’s fate all of this time, but now realizes that he was deceived and manipulated.
The Vilna Gaon says that the king whose fury subsided was H-Shem, King of the World. This may refer to the Zohar (III 133a), which translates the verse (Tehillim 144:15) that describes the Jewish people as “ha’am shekacha Lo,” or as “the nation that calms Him,” implying that the Jewish people have a tremendous power, if only we were to utilize it.
The Zer Zahav writes that Esther’s not forgiving Haman finally caused Shaul to be forgiven for taking unwarranted pity on Agag, Haman’s ancestor.
The Ginzei HaMelech writes that the Shir Ma’on quotes the Sha’aris Yisroel that quotes the great scholars who lived through the Chmielnicki Massacres of 5408-5409 (1648-1649 CE), which was one of the worst attempts at the genocide of the Jewish people in our history. They note that the large letter ches (Esther 1:6) and the large letter suf (Esther 9:29). Together, the letters spell out tach, a Hebrew way to reference the year 5408. This means that the massacre was a manifestation of Haman’s evil decree.
The Ginzei HaMelech heard from others the contention that the Chmielnicki Massacre was not the end of the effects of Haman’s decree. Rather, the Holocaust of tasha, 5705 (1945 CE), was the final manifestation of Haman’s decree. He proves this from the unique spelling of shachacha; since H-Shem was “calmed” about the Jewish people twice – once in tach, and once in tasha. There is proof of this in the mispar katan of the word shachacha (300+20+20+5=345= 12= 3) being the same as the mispar katan of tasha (400+300+5=705 = 12= 3). H-Shem is no longer anger.
The Ginzei HaMelech also quotes from Rav Michel Weissmandel that there is a hint to this in the traditional sizes of the letters in the list of Haman’s sons (Esther 9:7-9) as found in the Megillas Esther. The letters suf (400), shin (300), and zayin (7) there are smaller than the surrounding text, which refer to the year tashaz (1946 CE), the year in which ten Nazi officers were hanged at the Nuremberg Trials. There is also a large letter vuv (6), alluding to the sixth officer, Julius Streicher, who shouted “Purim Fest 1946” as he was being led to the gallows, despite the hanging taking place on Hoshana Rabba, the holiday on which the Zohar (III 31b-32a) says H-Shem judges the gentile nations. There was another Nazi who was supposed to be executed that day, Herman Goring, who committed suicide in his cell. He is likened to Haman’s daughter, who also killed herself. The comparison is extenuated by the fact that Goring famously enjoyed wearing women’s clothing.
Furthermore, the gematria of shachacha is the same as Moshe (40+300+5=345) because even good leaders are taken when H-Shem chooses to punish a generation. As the Talmud (Brachos 62b) teaches, a plague takes away the greatest of the generation together with the masses. Indeed, a storm sweeps away the good grain together with the chaff.
According to the Nachal Eshkol, another reason this gematria corresponds to Moshe is because the Midrash (Esther Rabba 6:2) says that yet another reason the Jews were saved from genocide was in the merit of Moshe. His merit should continue to be with us, and rescue us finally from this exile, bimheira biyameinu.
The Maharal notes that Haman’s advisers must have known that Mordechai was a Jew, as Haman, himself mentioned to them (Esther 5:13). After all, it was possible that Mordechai was brought into Persia with King Yechanya (Esther 2:6), but was not actually a Jew. Therefore, the Talmud (Megillah 16a) understands the advisers’ remarks as relating to Mordechai’s tribal lineage. In effect, they were saying that if he were from the tribe of Yehudah, Binyamin, Efrayim, or Menasheh, Haman could not expect to be successful against him. In Bireishis (49:8), Yaakov promised Yehudah that his descendants would conquer their enemies. In Tehillim (80:3), King David prays that H-Shem strengthen Efrayim, Binyamin, and Menasheh. As it happens, Mordechai could trace his paternal lineage to one of these listed tribes and his maternal lineage to another.
The Maharal points out that Yehudah, Efrayim and Binyamin all represent Jewish unity because the Beis HaMikdash, and the Mishkan in Shilo and Nov were all located in their tribal inheritance. As proof, the Maharal quotes from the verse (Bamidbar 16:6) in which Moshe attempts to quell the rebellion of Korach and his group by saying they should all bring fire-pans. The entire group bringing individual fire-pans would represent the very opposite of unity. In fact, the unity of Jews’ uniqueness with H-Shem’s Uniqueness fights off the doubts and confusion that Amalek represents. The Midrash (Esther Rabbah 6:2) considers the description “Yehudi” as being derived from the adjective “yechidi” (“unique”) or the noun echad, (“one”).
According to the Targum, the advisers were not asking if Mordechai was a Jew, but if he were from the holier, saintly Jews. The Vilna Gaon writes that, unlike Haman’s assertion that the events he described were chance, Zeresh and the advisers were saying that it was not. After all, as a member of the Yehudim, Mordechai enjoyed the situation promised by the Talmud (Shabbos 156a, Nedarim 32a) that “ein mazal b’Yisroel” (“there is not mazal for Israel”).
R’ Dovid Feinstein explains that the advisers were focusing on the fact that Haman’s situation could go either way, based on Jews’ behavior.
The Ginzei HaMelech quotes R’ Meir Shapiro, who focused on the word, “zerah” (“seed”). They were saying that if the Jewish youth had no serious connection to Mordechai. They considered the aged Mordechai only powerful if he still held relevant sway on the youth of his people. So when Haman told them that Mordechai was surrounded by thousands of students learning a (temporarily) outmoded law regarding grains and Temple service, the advisers realized Haman has no chance. When Judaism is relevant for the invigorated youth, our enemies stand no chance.
Similarly, says the Ginzei HaMelech, Mordechai has to be mizerah (“from the seed”) of Yehudim – an invigorated member of the youth in vitality – and then Haman should just give up.
According to the Ben Ish Chai, Haman gave a short history lesson saying Mordechai was a descendant of Shaul, who only ruled briefly and not successfully. In response, the advisers said, that may be true, but Mordechai was also a descendant of Yehudah from his mother’s side, so he will win as promised. Homiletically, he reads the word im (if) as eim (mother).