The input to the system is $ e^{2jt} $ which can be re-written as:
cos(t)+2jsin(t).
Its response to this signal is $ t*e^{-2jt} $ which can be rewritten as:
t*cos(t)-2j*sin(t)
Since the system is linear, the input of cos(2t) should yeild a result of:
t*cos(2t)
