Is the middle ring of this organic compound aromatic? Is the middle ring with 5 atoms of (4⁠Z)-4-[(4-methoxyphenyl)methylidene]-5-methyl-2-phenyl-2,4-dihydro-3⁠H-pyrazol-3-one aromatic?



The carbonyl group could become a negatively charged oxygen, the tertiary amine could then form a double bond with the $\ce C$ atom of the carbonyl group. The secondary amine could contribute one electron to the $\pi$-system. And the $\ce C$ atom of the ethen-group could contribute two electrons if the other $\ce C$ atom becomes positively charged, but I'm not sure if this is likely.
You don't have to force a positive charge on the carbon between the central and left rings.  The methoxy oxygen on the left ring can donate an electron pair to take up the positive charge.  The left ring then becomes quinoid and the central ring becomes aromatic.  Such switching between quinoid and aromatic rings is common in conjugated polycyclic structures.