Question

If a complex number z lies in the interior or on the boundary of a circle of radius 3 units and centre (– 4, 0), find the greatest and least values of |z +1| .

Answer 1

Distance of the point representing z from the centre of the circle is

According to given condition |z+4|≤3

Now 

|z + 1| = |z + 4 – 3| ≤| z + 4| +| −3 |≤3+3=6

Therefore, greatest value of |z + 1| is 6.

Since least value of the modulus of a complex number is zero, the least value of |z +1| =0