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  • The maximum value of | arg(1/1-z)|, z is a complex number

The maximum value of | arg(1/1-z)|, z is a complex number

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Solution: Put  \ omega =(1/1-z)

              \ omega =(1/1-z)Rightarrow z=(omega -1/omega )\ \Rightarrow left | z ight |=1Rightarrow left | (omega -1/omega ) ight |=1\ \Rightarrow left | omega -1 ight |=left | omega ight |

     Thus the locus of omega is the perpendicular bisector of the

   line segment joining 0 and 1 .

  \Rightarrow left | argomega ight |=pi /2 .

Posted by

Deependra Verma

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