Why the complex matrix cannot be restored?

I need to obtian a eigenvector and eigenvalue for a complex matrix B, and I have know that B=exp(iA), and A is also a complex matrix. I try use the matlab to solve this, but it seems can not work. My test process as follwoing:

%%%%%%%%%%

clc,clear

A=[1+2*1i,2-1*1i;
3+5*1i,4.5+7*1i];

B=exp(1i*A) %

[U,D]=eig(B);% for the element-by-element exponential

C=-1i*log(U*D/U);

D=-1i*log(B); % C must be equal to D, and D should be equal to A?

%%%%%%%%% the above cannot work, so I tried anothor one:

C=-1i*logm(U*D/U);

D=-1i*logm(B); % the results are odd.

I know that 'Eberlein 1970 Solution to the complex eigenproblem by a norm reducing Jacobi type method' have explain how to realize those, but it is a fortran code.

Does anybody has a matlab code? I'll be many thanks for your share.

[Jan]

Please do not let us guess what "cannot work" means. Do you get an error message or does the result differ from your expectations? A detailed explantion is required for an efficient answer.