What is the maximum value of |z| when z satisfies the condition |z+(2/z)|=2 ?

|z+ (2/z)|=2

1 Answer
Dec 29, 2017

|z|=sqrt2

Explanation:

There are two possible results of z(Let it be |z_a| and |z_b|). Then we have to decide which one is greater than the other and then the greater one is the answer.

+(z+(2/z))=2

(z^2+2)/z=2

z^2-2z+2=0

=>z_(1,2)=1+-i

|z_a|=sqrt(1^2+(+-1)^2)=sqrt2


-(z+(2/z))=2

(-z^2-2)/z=2

-z^2-2z-2=0

z^2+2z+2=0

=>z_(3,4)=-1+-i

|z_b|=sqrt((-1)^2+(+-1)^2)=sqrt2

|z_b|=|z_a|