Question

what did the rus do that led to the eventual influence of the byzantine empire on russia?
the rus forced the entire population to convert to the church of the byzantines.
the rus were originally from the area ruled by the byzantine empire.
the rus first invaded and then ruled over constantinople as well as the slavs.
the rus established a strong trading relationship with constantinople.

Explanation:

The Rus established a strong trading relationship with Constantinople, which led to increased cultural - economic exchanges and thus Byzantine influence on Russia. Forcing the population to convert (first option) is not accurate as it was more of a gradual adoption. The Rus were not originally from the Byzantine - ruled area (second option). And they did not rule over Constantinople and the Slavs in a way that led to Byzantine influence on Russia as described in the third option.

Answer:

The Rus established a strong trading relationship with Constantinople.