I'm trying to calculate the density matrix of the state $$|\psi \rangle=4|00\rangle + 3i|11\rangle -i|01\rangle + 2|10\rangle$$ 
And I've approached the problem by multiplying out $|\psi\rangle \langle\psi|$ with all the sixteen terms that gives me, and then worked out the matrix corresponding to the various different combinations like $|00\rangle\langle 00|$, $|01\rangle \langle 11|$ and so on, and turned the problem into matrix addition. 

As far as I know that works just fine, but it's exceptionally tedious to perform sixteen matrix multiplications! I do need to end up with a matrix, but is there a better way of approaching the problem?