clear

%HW 4:
%A)
% 6 points 
%but could use any n
n=6;
n2=floor(n/2);
for ip=1:(n2+1)
w(ip)=2*pi*(ip-1)/n;
end
sum=zeros(1+n2,1+n2);
for ip=1:(n2+1)
for jp=1:(n2+1)
for t=0:(n-1)
sum(ip,jp)=sum(ip,jp)+cos(w(ip)*t)*cos(w(jp)*t);
end
end 
end
sum
w

%B)
% 6 point
%if do not use i as an integer and clear previous variables, matlab will
%default to i=sqrt(-1)
n=6;
n2=floor(n/2);
for ip=1:(n2+1)
w(ip)=2*pi*(ip-1)/n;
end
sum=zeros(1+n2,1+n/2);
for ip=1:(n2+1)
for jp=1:(n2+1)
for t=0:(n-1)
sum(ip,jp)=sum(ip,jp)+exp(i*w(ip)*t)*exp(-i*w(jp)*t);
end
end 
end
sum
w