Apple do not make their own RAM. I have no idea where they buy it, but it is fair to say that RAM purchased from Apple will cost more than from anywhere else!
For reliable RAM puchase only from OWC/MacSales or Crucial. Both offer a lifetime warranty and will correctly identify the correct RAM modules for your Mac.
Apple has been using Hynix RAM for years.
iMac's are not all that picky about brand, but they are very picky about the RAM spec's.
as per > iMac (Mid 2011): Memory specifications your 2011 iMac uses PC3-10600 1333 MHz modules.
If the Corsair RAM Modules that you bought are the correct specs? Then you should have no problem install it along with the original factory 4GB and running a total of 20GB.
I would suspect that you are having one of three different problems.
1. The Corsair RAM is not the correct spec and while it works, it is causing errors and does not work when matched up with the factory RAM.
2. The Corsair RAM is the correct spec, but one of the modules is bad. (noting that: the way your holding that Hynix module is liable to damage it)
3. You are not pushing hard enough to fully seat the modules in the slots. (try pushing real hard on each module with both thumbs as you install them)
Going on that I would install the factory modules back in the original slots that they came in and test the iMac. Then if the Corsair modules are the correct spec, install them in the empty slots and test the iMac.
Then if you are still having a problem..? Like many other RAM suppliers, Corsair does have a life time warranty.
All the different RAM modules show up correctly when I select About my Mac. I also use Rember and didn't find any errors. After some lookups I didn't know what else to try.i took it an Apple certified tech and they said all their tests showed no problems. Of course they couldn't get it to lock up. He suggested I try repairing permissions, checking the drive and last option reinstalling OSX. (I'm still running Snow Leopard).
The Apple memory (pictured) is the same price as other brands. Original question is: should I buy it?