Would you be jealous if your gf/bf was talking with another person?

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I chat a lot with my girlfriend, but a few weeks ago it seemed like she was chatting with another person because she went a long time without say anything. She likes to chat a lot. When I asked about it once she told me. "It is Frank-san from Kansas. a young friend of mine from Canada, Eugene (he's in high school) and you:D, Frank is more like a brother that anything else... you're jealous again I think". I don't know what to think. I know she still loves me, but I am worried because before she was my girlfriend she chatted a lot with her ex-boyfriend, but when I started to chat with her like a friend I think she spent less time everyday talking to her ex-boyfriend until they broke up because they had different religions, and he needed to get married with someone whom his parents choose for him.