A system has the characteristics such that the input
x(t) = exp(2jt) yields the output y(t) = exp(-2jt)
and the input
x(t) = exp(-2jt) yields the output y(t) = exp(2jt).
What, then, is the system's output for the input signal x(t) = cos(2t)?
Well, it appears that the system produces the inverse of the input to provide the output signal, effectively dividing one by whatever the input signal is. If this is the case, then the input x(t) = cos(2t) will result in the output signal y(t) = 1/(cos(2t)). Also, we know that exp(2jt) = cos(2t) + jsin(2t) and exp(-2jt) = cos(2t) - jsin(2t) according to Euler's Formula.
