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If the imaginary part of z is 0, then z is simply a real number and if you multiply by 1 which is the identity in multiplication of real numbers, you of course will still have a real number with imaginary part 0

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Q: Let z be a complex number such that Imz 0 Prove that Im1z 0?
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Yes: The Two Two Boys formed in the late 60s in the Pilsen neighborhood on the corner of 22nd and California. When they formed in the late 60s, they were known as the 22nd Street Boys. By the year 1970, the Two Two Boys became a full fledged and recognized gang in Pilsen. In 1978 the 22nd Street Boys changed their name to the Two Two Boys as they joined the Folk nation alliance. The Two Two Boys were also one of the first gangs to join the Folk Nation in 1978 as they sided with the SDz. The Two Twos then became first cousins with the Satan Disciples. The Two Two Boys colors were brown and beige and still are. Even though Two Two main colors were brown and beige in the 70s, their war colors were always black and baby blue while their party colors were brown and beige. When the Two Two Boys formed they immediately found conflict with the following gangs: Latin Kings, Cullerton Deuces, Stone Kents, Villa Lobos, and the Coulter Kings. The Two Two boys had close relations to Satan Disciples and Ambrose and a small friendship with the Two Sixs. Up until about 1988, tags could be seen that read 226 meaning friendship with the Two Sixs or 224 meaning friendship with the Satan Disciples. In the early 1980s the Two Two Boys set their sites on Cicero and invaded the town attacking the gangs that were already there such as: Noble Knights, Twelfth Street Players, and Arch Dukes. The Two Two Boys soon swelled in numbers in Cicero immediately and helped wipe out the Arch Dukes in the early 80s. In a struggle for power, the Two Two boys battled heavily with the Noble Knights over Cicero. The two gangs dominated Cicero all throughout the 1980s. interalliance trouble came for the Two Two Boys in 1988 between them and the Two Sixs, when a Two Two Boy was having sexual relations with a Two Sixs girlfriend behind his back. 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In the Fall of 1994 as Milwaukee Kings moved in to Cicero, they started a war with the Two Two Boys by killing a Two Two Boy, which then caused the Two Twos to retaliate. In 1994 the Two Two Boys and Cullerton Deuces squashed their beef right after CDs became Folks in 1994. The alliance between CDs and Two Twos was short lived, by 1996 or 1997, the two gangs were back at war. In 1996 the Two Two Boys went to war with Laraza. In the year 2002 an incident occurred between the Simon City Royals and the Two Twos that resulted in murder. The Royals were visiting the area of 22nd and California which is Two Two Boy stronghold. During this visit, a conflict occurred between 22s and SCRs as the SCRs came to the hood to call out the 22s, the 22s responded by shooting a high ranking Royal in the head. The Two Two that fired the gun was arrested and convicted of second degree murder. Now Two Twos and Royals are at war since 2002... From Chicagogangs.org