The response of the system to $ e^{2jt} $ is $ te^{-2jt} $ and $ e^{-2jt} $ is $ t e^{2jt} $
We are asked how the system will respond to cos(2t)
By Euler's formula we know cos(2t) = $ \left ( \frac{1}{2} \right )(e^{2j} + e^{-2j}) $
the response to the system should be $ \left ( \frac{1}{2} \right )t(e^{-2j} + e^{2j}) $
which is tcos(2t)
