1.
If α\alpha denotes the number of solutions of z2=2iz^2 = 2i in the interval 0≤arg⁡(z)≤2π0 \le \arg(z) \le 2\pi and β=∣arg⁡(z)∣\beta = |\arg(z)| where z=(1+i)(1−i3)(1−i)z = \dfrac{(1+i)(1-i\sqrt{3})}{(1-i)}, i=−1i = \sqrt{-1}, then the distance of the point (α,β)(\alpha, \beta) from the line 4x−3y=74x - 3y = 7 is: