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Tunka-Rex is a new radio antenna array which extends the Tunka experiment in Siberia close to lake Baikal. It consists of 20 antennas on an area of 1km2 which measure the radio emission of high-energy air showers. Tunka-Rex is triggered by the photomultiplier array of Tunka measuring air-Cherenkov light of air showers in the energy range from about 1016 eV to 1018 eV. This configuration allows for the worldwide first hybrid measurements of the radio and air-Cherenkov signal for the same events: an ideal situation to perform a cross-calibration between both methods. Consequently, the main goal of Tunka-Rex is to determine the achievable energy and Xmax precision of radio measurements by comparing them to the reconstruction of the air-Cherenkov measurements. Tunka-Rex started operation in autumn 2012, and already detected air-shower events. In this paper we present the status of Tunka-Rex and first results which indicate that Tunka-Rex measures indeed the radio emission by air showers and that is is sensitive to their energy