Question

If |z+1/z|=a then find the maximum and minimum values of |z|

Answer 1

|z+1/z|=a.

|z|+1/|z| <=a

Let z=x+iy

√(x²+y²) + 1/(√x²+y²)<=a


(x²+y²) + 1<=a√(x²+y²)

|z|²+1 <=a²|z|
|z|²<=a²|z|-1
|z|²-a²|z|<=-1
|z²|-a²|z|+1<=0

Solve equation to get the corresponding values.