Aims. We selected two radio quasars (J1036+1326 and J1353+5725) based on their 1.4-GHz radio structure, which is dominated by a bright central core and a pair of weaker and nearly symmetric lobes at ~10 angular separation. They are optically identified in the Sloan Digital Sky Survey (SDSS) at spectroscopic redshifts z>3. We investigate the possibility that their core-dominated triple morphology can be a sign of restarted radio activity in these quasars, involving a significant repositioning of the radio jet axis. Methods. We present the results of high-resolution radio imaging observations of J1036+1326 and J1353+5725, performed with the European Very Long Baseline Interferometry (VLBI) Network (EVN) at 1.6 GHz. These data are supplemented by archive observations from the Very Large Array (VLA).We study the large- and small-scale radio structures and the brightness temperatures, then estimate relativistic beaming parameters. Results. We show that the central emission region of these two high-redshift, core-dominated triple sources is compact but resolved at ~10 milli-arcsecond resolution. We find that it is not necessary to invoke large misalignment between the VLBI jet and the large-scale radio structure to explain the observed properties of the sources.
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