If `|z-25i|le15` , then find
(i) Maximum |z| (2) Maximum arg (z)
(3) minimum |z| (4) Minimum arg (z)

Explanation

First of alll we plot the region represented by the complex number satisfying , ` |z -25i|ge 15` in the Argand plane. Clearly the given inequation represents all the points lying on as well inside the cirle centred at C( 0,25) and radius 15.
form, figure it is transparent that
Minimum |z| = OQ = 25-25 =10units
Maximum |z| = OQ = 25+ 15 = 40 units
In ` triangle OCP, OP = sqrt(25^(2)-25^(2)) = 20 `
`tan theta = 20 /15 = 4/3`
Minimum argument of ` z = angleXOP = tan^(-1)(4/3)`
Maximum argument of ` z= angleXOP,= pi - tan^(-1)4/3`