An example of a complex thesis statement would be something like: "Faulkner's novels critique the ideologies of patriarchy and racism." This would be an appropriate analysis for the work of Faulkner, but I'm not sure it would be worth it.
To begin with, it is not clear what the writer has to gain in terms of proving BOTH of these aspects of the work rather than just the one.
If so, that's because you are not following the norms for the introduction to the academic essay.
Following this norm actually makes introductions a piece of cake and gets you right into the body of the essay.
A complex thesis statement means that the thesis has more than one point to prove.
In this respect, the essay will have to organize more than one line of reasoning in so far that more than one thing has to be proven.
Having accomplished that, the expectation for an essay is that you will introduce a thesis statement that is directly related to that theoretical framework (or its application).
As a result, a major convention of the academic essay is that: Having stated a thesis, you are expected to then go and prove it through the body of the essay.
With this in mind let's examine how to write an academic essay.
Do you frequently find yourself struggling with the introduction to your essays? Do you find yourself searching for a generalizing statement that will get things going, and trying to find a delicate balance between BS'ing and saying something meaningful?