Q: Connecting a Iiyama 27' monitor to an iMac

After checking with the supplier that it would work with my very recent iMac (OS 10.9, 4 Gb graphic card) , I bought a Iiyama 27 inches monitor with a 2560x1440 pixel resolution to use as a second monitor in dual mode.

I tried to connect this monitor to my iMac using 1st/ a minidisplay to DVI adapter and later, with a recommendation from Apple Care 2nd/ a minidisplay to HDMI Moshi adapter.

In both cases, I get a picture on the display, but I cannot get the full resolution. The monitor supplier (namely Pixmania.com) is hopeless, so I try the Apple community as there has to be a number of people who chose this Iiyama monitor as a companion to their iMac – not as shinny but substantially cheaper than the Apple display.

Question is therefore: how do I get this monitor to display at full resolution in a dual monitor config? What kind of cable / adapter do I need? Has anyone successfully tried it?

Thanks