As background, spend some time experimenting with the properties of complex exponential sequences
x[n] = z^n
or in MATLAB terms
x = z.^n
where z is an arbitrary complex number, and n ranges over integers.
In the general case, we think of n as running from minus infinity to infinity, but obviously for explorations in MATLAB you'll look at specific finite sequences of values of n. I suggest that you focus on sequences like n = 1:100 and the like, though understanding the properties of other index ranges is fine as well.
Then write a MATLAB function whose inputs are a complex number z and a (finite) impulse response h, and whose output is the (complex) constant H(z) that is the "eigenvalue" for the complex exponential z^n and the shift-invariant linear system defined by h.
Here is a set of hints intended to point you in a plausible direction.