Prove that if n = 12 and G is a simple graph on n vertices, then it is not possible for both G and the complement of G to be planar.

I know that:

for a graph to be non planar we have to either find a subgraph isomorphic to k5 or k3,3 or a subdivision of k5 or k3,3

and I know that complement of G is connected if G is a graph on n vertices where n>= 2

but I'm not sure if I'm on the right track and how exactly to combine these ideas to come up with a solid proof.