“If you have a {{w|complex manifold}}, if the {{w|manifold}} you are studying is complex, then... [by] Hodge... [etc.,] the differential forms on the manifold can be broken up into the forms of type (p,q) where p involves the dz's and q involves the d\bar{z}'s, the mixture of the two [is] the {{w|tensor product}}. So when you have a complex structure, you see the square root, and the square root is complex geometry. So when you have complex geometry, you've found the square root inside the real geometry. Complex structure has given you the square root.”