Why can't I get the complex sulotion

cvx_begin quiet
variable V(N+1,N+1) hermitian semidefinite
dual variables y
maximize (real(trace(X11V)));
subject to
-r1
sigma+real(trace(X11V))>=0;
-r2
sigma-r2real(trace(X11V))+real(trace(X12V))>=0;
-r2
sigma-r2real(trace(X21V))+real(trace(X22V))>=0;
%-real(trace(w1
w1’))-real(trace(w2*w2’))+Pt>=0;
1- norm(V)>=0;
y: V semidefinite(N+1);
cvx_end

I tried to declare the variable V as “complex”, “complex semidefinite” and “hermitian semidefinite”. But I always get the “double” type of V. Why and How can I get complex solution fo V?