% [b] Using the build in function for polynomial root computation we verify
% the roots that we got in section [a]:
r= roots([1,0,0,0,-16]);
disp(r);
% [c] By making a figure in the complex plan,that connects all four roots that we optain in [b] in a loop and which
% goes from a root which has the real part equal to zero to a root that has
% the imaginary part equal to zero or vice versa we optain a plot which shows
% that the four roots are positioned on the vertices of a square:
plot(([r(1),r(2),r(4),r(3),r(1)]),'-o');
% plots the roots in the right order (for example could also be [r(2),r(4),r(3),r(1),r(2)]) to make a square and adds a small
% circle around each root
grid;
% colours the background of the plot with squares with side of length of
% one unit
title('Argand diagram');
% labels the diagriam
xlabel('Real axis');
% labels the x axis of the diagram
ylabel('Imaginary axis');
% labels the y axis of the diagram
% [d] To get the length of a side of the square that we got in the plot of [c] we need
% to calculate the modulus of the complex number that we get taking the difference of two consecutive complex
% numbers that were used to obtain the plot.
abs(r(1)-r(2));
% could also be abs(r(2)-r(4))