If α denotes the number of solutions of |1-i|^x=2^x and β=((|z|)/((z))), where z=(π)/4(1+i)^4[(1-√ π i)/(√ π +i)+(√ π -i)/(1+√ π i)], i=√ -1, then…

If $\displaystyle \alpha$ denotes the number of solutions of $\displaystyle |1-i|^x=2^x$ and $\displaystyle \beta=\left(\frac{|z|}{\arg (z)}\right)$, where $\displaystyle z=\frac{\pi}{4}(1+i)^4\left[\frac{1-\sqrt{\pi} i}{\sqrt{\pi}+i}+\frac{\sqrt{\pi}-i}{1+\sqrt{\pi} i}\right], i=\sqrt{-1}$, then the distance of the point $\displaystyle (\alpha, \beta)$ from the line $\displaystyle 4 x-3 y=7$ is $\displaystyle \_\_\_\_$