The set of all α ∈ R, for which w =(1+(1-8 α) z)/(1-z) is a purely imaginary number, for all z ∈ C satisfying |z|=1 and Re z ≠ 1, is:

The set of all $\displaystyle \alpha \in \mathbf{R}$, for which $\displaystyle \mathrm{w}=\frac{1+(1-8 \alpha) z}{1-z}$ is a purely imaginary number, for all $\displaystyle z \in \mathbf{C}$ satisfying $\displaystyle |z|=1$ and $\displaystyle \operatorname{Re} z \neq 1$, is :