Solution:

$ \begin{aligned}\\ \dot{y}(n) &=x(n) * h(n) \\\\ x(n) &=\{1,1,1,0\} \\\\ h(n) &=\{-1,-1,0,0\} \\\\ g(n) &=x(n)+j h(n) \\\\ &=\{1-j, 1-j, 1,0\}\\ \end{aligned}\\ $

$ \begin{aligned}\\ G(k) &=\sum_{n=0}^{N-1} g(n) e^{-j 2 \pi / N n k} \\\\ &=\sum_{n=0}^3 g(n) e^{-j \pi / 2 n k} \\\\ G(0) &=\sum_{n=0}^3 g(n) e^0=1-j+1-j+1=3-2 j\\ …