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

#|z+ (2/z)|=2#

1 Answer
kubik98
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|#

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