On the conjugacy of pure imaginary elements of quaternion algebras and Cayley algebras

In the quatenions (\H, \H', \H^{C}) and octonions ($\text{gC}$, ${\text{gC}}^{\mathrm{\prime }}$, ${\text{gC}}^C$), we show some results on the conjugacy of two pure imaginary non-zero elements with same norm.