1.If α\alphaα denotes the number of solutions of z2=2iz^2 = 2iz2=2i in the interval 0≤arg(z)≤2π0 \le \arg(z) \le 2\pi0≤arg(z)≤2π and β=∣arg(z)∣\beta = |\arg(z)|β=∣arg(z)∣ where z=(1+i)(1−i3)(1−i)z = \dfrac{(1+i)(1-i\sqrt{3})}{(1-i)}z=(1−i)(1+i)(1−i3), i=−1i = \sqrt{-1}i=−1, then the distance of the point (α,β)(\alpha, \beta)(α,β) from the line 4x−3y=74x - 3y = 74x−3y=7 is:a.15\dfrac{1}{5}51b.25\dfrac{2}{5}52c.35\dfrac{3}{5}53d.45\dfrac{4}{5}54Login to continueOnly logged in users canattempt or see the solution.
