Where did I go wrong in this Euler Proof

Question

Why are the two proofs below contradicting each other?

• $e^{iπ} = -1 $
• $e^{π2i}= (e^{iπ})^2 = 1$
• $(e^{π2i})^π = 1$

Part 2

• $(e^{π2i})^π = e^{{π^2}2i}$
• $cos(2{π^2}) = i sin(2{π^2})$ ≠ 1