%% Problem (a)

t = [0:0.1:10];
y = exp(t*(3i-0.5));
plot(t,real(y))

%% Problem (b)

A = [ 0 i;i 0];

B = [0  1 0;...
     1  0 i;...
     0 -i 0]*1/sqrt(2);
 
C = 1/2*[...
    1  1  1  1;...
    1 -1  1 -1;...
    1  1 -1 -1;...
    1 -1 -1  1];

% check if hermitian
A-conj(transp(A))
B-conj(transp(B))
C-conj(transp(C))

% check if unitary
A*conj(transp(A))
B*conj(transp(B))
C*conj(transp(C))
 
% trace
trace(A)
trace(B)
trace(C)

% eigenvalues
eig(A)
eig(B)
eig(C)
