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If the square root of \(\frac{x^2}{y^2} + \frac{y^2}{x^2}+ \frac1{2i} (\frac yx + \frac xy) + \frac {31}{16} \) is \(\pm(\frac xy + \frac yx - \frac im)\), then m is

a. 2

b. 3

c. 4

d. none of these

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