Why do you think there might be any imaginary parts?
Try this:
t = linspace(-2*pi, 2*pi, 1000);
x = cos(t/4)+cos(3*t/4);
plot(t, x, 'b-', 'LineWidth', 2);
grid on;
xlabel('t', 'FontSize', 20);
ylabel('x', 'FontSize', 20);
but if t were complex, you could plot real(x) and imag(x) instead of x.
