The shaded area on the argand plane if $|\bar z + zi| \leq 2$. and find the maximum value for $Arg(z)$
My attempt:
Let $$z=x+iy$$ $$|(x-iy)+(x+iy)i| \leq 2$$
Then $$|(x-iy)+(xi-y)|\leq 2$$
so we get $$x-\sqrt2 \leq y \leq x+{\sqrt2}$$
Then how can I determine the maximum value for $Arg(z)$?
Is there a geometrical method instead of $z=x+iy$ ?