About SOCP programming

I want to solve my problem with this model.
and for complex data, it is suggested to use SOCP frame programming to solve it. But i just write it like it in the picture and work it out. So i am confused that why i can get the result with the form in the picture but not SOCP framework. Did CVX transfer it to SOCP framework automatically or do some other transfermations for the object function?

Yes, CVX will convert it to SOCP for you.

OK,thank you for your answer