The City of Rockville is planning an $82 million office and hotel complex that city officials hope will set the stage for the downtown area for the next half-century.

The project, planned for completion by 1989, also should help the neighboring Rockville Mall, many of whose stores have been vacant for months. City officials said hearings must be held before the project can be approved.

"I'm absolutely convinced the mall will be a success and make a lot of money for someone," said Rockville Mayor William E. Hanna Jr. "Between the Metro subway station , the county office building and this first-class development," the mall should pull out of its slump, he asserted.

A new 12-story, 250-room hotel is planned for development by 1984 on a 2.38-acre site at Courthouse Square near the corner of Washington Street and Middle Lane. The proposed developer, a partnership of Winmar Co. and Nordal Associates, also plans 80,000 square feet of office space and an open-air plaza on the site.

The 675,000-square-foot office complex on Middle Lane across from Rockville Mall will be built over a five-year period beginning in 1984 . When completed in 1989, it will have three office buildings ranging in height from 10 to 20 stories, ground-level retail space and enclosed parking.

Between 1982 and 1989, the city expects to pay about $500,000 for traffic improvements, part of the Middle Lane pedestrian overpass, demolition of a building on one of the sites and maintaining a park near the office complex. However, during the same period, the city also projects revenues of $3.6 million from the sale or lease of the two sites, construction fees and permits, storm water management contributions and real estate and personal property taxes.