9. If , where and are real, find the
   values of and if

To find the values of and for , we start by expressing the equation .

We know that . Thus, we can rewrite the left-hand side \(\frac{1}{z}\) and \(\frac{2}{\bar{z}}\) as follows:

Now, substituting into the original equation gives:

Combine the fractions:

This simplifies to:

Equating real and imaginary parts leads to:

From the second equation, we can solve for :

Rearranging gives:

Now, using the first equation:

Substituting from the rearranged second equation into the first gives:

Now we substitute back into this equation or utilize it to express in terms of . Solving both equations will yield the values for and .

However, we can also directly substitute and solve the quadratic formed by plugging in values or deriving solutions through algebraic substitutions which yields:

Thus .