Why am I getting the complex number in the for loop?

I was trying to compute a matrix of values using the following codes (simplified):

n = 5;
xk = zeros(n+1);
for i = 0:n
    Tempprod = 1;
    for j = 0:n
        xk(i+1,j+1) = cos(pi*(2j+1)/(2*(n+1)));
    end
end

The output of the above code is

xk =

   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i
   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i
   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i
   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i
   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i
   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i   1.1014 - 0.1418i

However, if I tried to compute one single value, say , I tried

    cos(pi*(2*1+1)/(2*(5+1)))

and Matlab gave me the answer:

    ans =

        0.7071

So what I went wrong in the codes before? How can I fix it?

Answer 1

[Fangjun Jiang]

Try not to use variable name i and j. Try this

clear all
i
j

or you missed one "*"

cos(pi*(2*j+1)/(2*(n+1)))

[Zhuoyi Chen]

Thanks!!