Why are real orbitals used to define the orbital of hydrogenic atoms instead of complex orbitals? On the physics site, I asked the difference between real &amp; complex orbital. Real orbitals are the superposition of complex orbitals having definite magnetic quantum number states.

\begin{align}
p_z &amp;= p_0 \\
p_x &amp;= \frac{1}{\sqrt{2}} \left(p_1 + p_{-1} \right) \\
p_y &amp;= \frac{1}{i\sqrt{2}} \left( p_1 - p_{-1} \right)\\
\end{align} 
where $p_0 = R_{n1} Y_{10}$, $p_1 = R_{n1} Y_{11}$, and $p_{−1} = R_{n1} Y_{1−1}$, are the complex orbitals corresponding to $\ell = 1$.

My question is:  

Why aren't the orbitals of hydrogenic atoms taken as complex orbitals instead of the real ones? They are valid states for an electron, aren't they? So, what is the problem in having complex atomic orbitals?
The main disadvantage of complex atomic orbitals (AOs) is that many of them are hard to visualize.  For example, try making a simple sketch explaining how $p_{-1}$ differs from $p_{1}$. Conversely the complex AOs have very few  advantages over real MOs - they are all eigenfunctions of $\hat{L}_z$ but that's not really important for molecular  and closed shell systems. 

So with many key advantages and very few disadvantages real orbitals are understandably the most popular choice.