Sol. The complex numbers satisfying the condition

.......(i)

are represented by the points inside and on the circle of radius 15 and center at the point .
The complex numbers having least positive argument and maximum positive arguments in this region are the points of contact of tangents drawn from origin to the circle.
Here, Least positive argument
and Maximum positive argument

∴ In

and

Thus, complex number at has modulus 20 and argument

From the figure, is the point with least modulus and is the point with maximum modulus.
Hence,
and

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