I am unable to verify the fact that the complexification of the real lie algebra $\mathrm{sp}(m,n)$ is $\mathrm{sp}(2(m+n),\mathbf C)$, where $\mathrm{sp}(m,n)$ is the set of endomorphisms preserving the Hermitian bilinear form over the quaternions and $\mathrm{sp}(2n,\mathbf C)$ is the set of endomorphism preserving the skew symmetric bilinear form over complex numbers. It will be helpful to me if some one tell me some source.
I verified that complexification of $\mathrm{sp}(m,n)$ is isomorphic to a conjugate of $\mathrm{sp}(2n,\mathbf C)$. I want to find that matrix which conjugate $\mathrm{sp}(2n,\mathbf C)$ and complexification of $\mathrm{sp}(m,n)$.
A brief (but sufficient!) justification is given in William Fulton, Joe Harris, Representation Theory: A First Course. Springer-Verlag, $1991$.
Edit. It seems you also got an answer for this question over at MathOverflow?