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# mod(Z-25i)<15 then diffrence of min,max of argZ

Akash Kumar Dutta
98 Points
8 years ago

Dear Mahendra,

mod (Z-25i)<15,
means Z lies in the circumference of the circle with (0,25) at its centre and radius less then 15.
so difference in the max and min value of arg Z is given by the angle between the common tangents to the circle from origin.
the length of the tangents are 20 units( root  [(25)^2 - (15)^2])
hence the angle between y axis and a tangent is tan inverse (15/20) = tan inverse 3/4=37 degree.
hence the total diff. = angle between the tangents = 2 times the angle between the y axis and one of the tangents.
=2.37=74 degree or 2.[tan inverse 3/4]
= 74 degree or [tan inverse (24/7) ]
(ANS)

Regards.