SOLUTION: if |z|=3 then determine the least value of |z+1/z|=

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Question 242873: if |z|=3 then determine the least value of |z+1/z|=
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

abs%28z%29=sqrt%28x%5E2%2By%5E2%29=3, so x%5E2%2By%5E2=9 and y%5E2=9-x%5E2



Therefore:





This is a minimum when x=0, thus

abs%28z%2B1%2Fz%29 has minimum value %282%2F3%29%28sqrt%280%5E2%2B16%29%29=%282%2F3%29sqrt%2816%29=%282%2F3%29%284%29=8%2F3

Edwin