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, we know that exp(2jt) = cos(2t) + jsin(2t) and exp(-2jt) = cos(2t) - jsin(2t) according to Euler's Formula.
