Consider a complex scalar field $\psi(x)$ with Lagrangian density
$$ \mathcal{L} = \partial_\mu\psi^* \partial^\mu\psi - M^2\psi^*\psi. $$
Expand the complex field operator as a sum
$$ \psi = \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2E_\mathbf{p}}}(b_\mathbf{p}e^{i\mathbf{p}\cdot\mathbf{x}} + c_\mathbf{p}^\dagger e^{-i\mathbf{p}\cdot\mathbf{x}}). $$
From the Lagranigan density we obtain the momentum $\pi = \dot\psi^*$. From the above information, how do we derive the expression for $\pi$:
$$ \pi = \int \frac{d^3p}{(2\pi)^3} i \sqrt{\frac{E_\mathbf{p}}{2}} (b_\mathbf{p}^\dagger e^{-i\mathbf{p}\cdot\mathbf{x}}- c_\mathbf{p} e^{i\mathbf{p}\cdot\mathbf{x}})~? $$