Baran's Quaternionic Euler-Like Identity (e^(i+j+k)/√3+1=0.

This work introduces a quaternionic identity inspired by the classical Euler identity. The formulation extends the exponential structure to the quaternionic direction defined by the normalized vector (i + j + k)/√3. The expression e^((i + j + k)/√3) + 1 = 0 is presented as an Euler-like relation in quaternionic space. The identity highlights a symmetric direction in quaternion algebra and provides a compact exponential representation analogous to the well-known complex Euler identity. This construction is proposed as a new perspective connecting quaternion exponentials with Euler-type identities and is introduced by Abdullah(Edvîlla) Baran.