MATLAB can find determinants. Here is an example.
>> A=[1,3,2,4;-5,7,2,3;2,3,7,11;1,2,3,4]; det(A)
Then press enter and you get
To enter a complex number 1 + 2i for example, you type: complex(1,2). However, when matlab gives the answer, it will write it in the usual form 1 + 2i. If you have matrices in which there are complex entries, you can go ahead and let matlab do the tedious computations for you.