a circle at point
with radius 2
The minimum value of mod(z) is the smallest distance from the origin to the circle
(look at picture)
To find x, simply use Pythagoras' theorem.
So minimum value = Distance from origin to center - Radius
= 4 - 2
= 2
For your next question I'm not too sure, but I'll give it a go.
(full speculating here lol.)
Max value of Arg(z) is the angle from the positive x-axis to the point on the circle producing the largest angle. (ie. a tangent)
Looking at pic2, and knowing that a tangent to a circle produces a right angle with the radius from the center we can find the angle.
From previous question we have x = 4
the angle between the red and green line (lol) is:
I'm not entirely sure on either these answers, need confirmation.