The shooting occurred at about 7 a.m. near the intersection of 8th and Fresno streets, according to the Los Angeles Police Department.
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The victim was identified as Jose Fernando Arellano, 31, from Bloomington in San Bernardino County.
Authorities said Arellano was visiting a friend at the complex, and when he was approaching his car, a four-door, dark-colored vehicle with two people inside pulled up next to him.
The victim and a passenger of the vehicle exchanged words before the suspect opened fire and fled. Witnesses reported hearing five to six shots.
Arellano died at the scene, according to the coroner's office.
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Police said the shooting does not appear to be gang-related, and no arrests have been made.
It was not clear if the suspect and victim knew each other prior to the encounter.
A description of the suspects in the shooting was not available. Anyone with information was urged to contact the LAPD's Hollenbeck Station.