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Gogeta wears the same clothes that all creations of the Fusion Dance wear. However, Gogeta's vest has a different color scheme than Gotenks'. The padding around the neck and shoulders of the vest is reddish orange rather than yellow, and the rest is either a very dark blue or a dark gray. The hair is very similar to Vegito's, with the only differences being that Gogeta only has one free hanging lock of hair instead of two and Gogeta having Vegeta's widow's peak. Although they are made in the very same way, Gogeta has personality traits that are different from Gotenks, though it is impossible to tell which counterparts' personality is the dominant one. And since his appearances have been limited and short, it is difficult to tell if his personality is a separate one, or a composite of both Goku and Vegeta. Although at Super Saiyan 4 it seems that his personality leans more towards Goku. Gogeta possesses Goku's body structure, he is tall and slender, but he seems to mostly possesses Vegeta's facial features. Super Saiyan 4 Gogeta can be equally serious as his Super Saiyan 1 form or more if he needs to.
Gogeta is formed by the merging of two powerful Saiyans, Goku and Vegeta, via the Fusion Dance. He is the second fusion performed through the Fusion Dance during the Dragon Ball Z series. He, like his fusion son Gotenks, was a desperate fusion done to defeat a powerful enemy; Gogeta's enemy was Janemba in DBZ and Omega Shenron in GT. Unlike Gotenks, who is seen many times during the saga with Majin Buu, in Dragon Ball Z, Gogeta is seen only twice in non-canon appearances, once in Movie 12 (Fusion Reborn) and during the final battles of the Anime Exclusive Dragon Ball GT series.
In Fusion Reborn, Gogeta made an appearance during the end of the movie. After Janemba transformed into his Super Form and became too powerful for Goku and Vegeta to handle, Goku quickly taught the Fusion Dance to Vegeta. The Fusion Dance must be performed perfectly to create a powerful warrior, so when Vegeta failed to extend his index fingers in the final step of the dance, the weak 'Veku' was created. The second time around, the Fusion Dance was performed correctly, and Gogeta was born. He easily overpowered and killed Janemba with the Soul Punisher.
During Dragon Ball GT, Goku and Vegeta fused into Gogeta at Super Saiyan 4 to fight Omega Shenron. He easily overpowered him and even played around with him. However, Gogeta spent too much time goofing around and the fusion ended before he could finish him off.
Although it has been stated that the Potara fusion is stronger than Fusion Dance in the original manga, Gogeta clearly surpasses Vegito in Dragon Ball GT when he is a Super Saiyan 4. However, Vegito was created during the Majin Buu Saga when Goku and Vegeta were much weaker than they were in GT. If Goku and Vegeta had fused into Vegito in GT, the result would possibly be even more powerful than Gogeta.
Veku
The fat version of Gogeta. This occurred when Goku and Vegeta attempted to fuse with the fusion dance in Movie 12 for the first time. Vegeta fails to extend his index finger, resulting in a bad fusion, forming a fat, incredibly weak fighter who was called Veku by South Kai. In this form, speed is decreased, and ki is limited to the point where it is ridiculous to even try to fight. Veku, because of his state, is unable to perform any ki attacks due to the drop in power. And because of his fat body, he cannot retaliate by punching and kicking. Instead, all he can do is pass gas, which he uses against Janemba to try and escape him. Just like a regular fusion, the time is 30 minutes before the two fighters defuse. This type of failed fusion is also seen in Goten's and Trunks' during the Majin Buu Saga, where they formed Fat Gotenks when attempting to fuse for the first time.
Super Saiyan
This form is seen during DBZ Movie 12. Immediately after the successful fusion dance of Goku and Vegeta, Gogeta is at Super Saiyan as both halves (Goku and Vegeta) had previously mastered the transformation. Even though Janemba easily took care of Goku at Super Saiyan 3 and Vegeta at Super Saiyan 2, he was unable to even hurt Gogeta at all. (A full force punch from Janemba to Gogeta's face didn't do anything.) In a matter of seconds, Gogeta was able to destroy Janemba without any problem whatsoever. While at this stage, he is exponentially stronger than Vegeta at Super Saiyan 2, and Goku at Super Saiyan 3, and is likely the strongest character in any of the 13 Dragon Ball Z movies.
Super Saiyan 4
This stage is seen in Dragon Ball GT, where Goku and Vegeta both faced off against Omega Shenron. With the Fusion Dance, they successfully created the mighty Super Saiyan 4 Fusion. Unlike Vegeta and Goku's Super Saiyan 4 form, the Super Saiyan 4 Fusion form has brown fur and fiery orange hair, instead of the opposite, and he is the only Super Saiyan that features blue eyes (without a strong green hint) as well. He is also the only character in the series with glitter in his energy aura. Compared to his more serious Super Saiyan form, the Super Saiyan 4 Fusion is somewhat more playful and wacky (almost akin to Vegetto's attitude), toying with the evil Omega Shenron instead of easily defeating him, possibly because the power was going to his head, though Vegeta states that Goku was in fact responsible for this behavior. It could be implied that Gogeta's personality may be based on a combination of Goku's youthfulness and Vegeta's arrogance. That, however, is only speculation. It is also implied he was only doing this so Omega Shenron would use a Negative energy based attack which Gogeta could use to cure the planet of Omega Shenron's evil energy. This is likely, as Gogeta immediately tries to destroy Omega Shenron afterward. His speed in this form is the greatest seen in the series, being so fast not even the viewer can see his movements. Many of his strikes appear as simple twitches, if anything. Along with his incredible speed, Gogeta also harbors an enormous amount of power and energy. As a Super Saiyan 4, Gogeta is immeasurably powerful. In fact, Gogeta in his Super Saiyan 4 form is seemingly invincible due to the immense power level gap between him and all other characters in the series. His only weakness is his inability to stay fused for longer than 10 minutes due to the ridiculously high amount of power he possesses. With so much amazing speed and power at his disposal, Super Saiyan 4 Gogeta is easily the most powerful character in the series, surpassing even the most powerful characters like Super Saiyan 4 Goku, Super Saiyan 4 Vegeta, Ultimate Gohan, Legendary Super Saiyan Broly, Majin Buu, Super Android 17, Omega Shenron, and everyone else in the whole anime.