The following functions are specified as the real part of

Question

The following functions are specified as the real part of impedance function Z(s).

Find the function Z(s).

a) R(w)  = 16 - 8w² + w⁴ /1 +w⁸

b) R(w) = 2 + 4w²  + 3w⁴  + w⁶ / 1 +  w⁸

c) R(w) = -w²  + 2w⁴ -w⁸/1 + w⁸

d) R(w) = 1- 2w²  + w⁴ / 1- 2w² + w⁴  + 4w⁶

e) R(w) = (1- w²  + w⁴)² /(w²⁴  - 4w² + 3)² + w²( w⁴ - 6w² + 8)²