I lived in Zurich for a year and a half without knowing much German/Swiss-German. It's very possible to live there without knowing German. Zurich is a big city with a lot of business and foreign workers so you'll have no issue in the city.
The further you go outside the center, it gets difficult very quickly. A lot of older residents who didn't move to Zurich for business reasons and didn't have English as part of their education aren't very confident with their english.
If you want to venture outside Zurich, you'll want to be able to get by with German/Swiss German. If you want to hang around the city with other 20–30 year olds, you'll be fine. Zurich is amazing in the summer, the river and the Flussbads are my favourite places.