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ISI2015-MMA-83

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If $\alpha, \beta$ are complex numbers then the maximum value of $\dfrac{\alpha \overline{\beta}+\overline{\alpha}\beta}{\mid \alpha \beta \mid}$ is

  1. $2$
  2. $1$
  3. the expression may not always be a real number and hence maximum does not make sense
  4. none of the above
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Answer: C

------------------------------------------------------------

$\alpha=1,\beta=\iota$

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