We show that writing the time coordinate of spacetime as W = iτ — purely imaginary in the complex sense — on the real axis of Hamilton’s Quaternion, and placing the three spatial coordinates on the three Quaternion-imaginary axes ι, j, k, produces a complex Quaternion whose norm is the Lorentzian spacetime interval without postulate. The complex unit i and the Quaternion units ι, j, k are independent: their squares both equal −1 but they are not the same −1.