In my exercise book I couldn't find a way to solve what I've typed below (I know for final solutions anyway):

PROBLEM 1

Find Re(w) and Im(w) [where

]:

So we have to write a complex number in a standard form and then extract a real and an imaginary part from there. We work here with the unknown variables (

and

).

My way would be:

If I expand the expression further (i.e. numerator) I don't find a way to write it in a standard form.

However, the final solution is:

and

Does anybody know the steps leading to the final solution?

PROBLEM 2

Find all solutions to the equation [where

]:

It is a quadratic equation and has a conjugate of complex number in it.

Thanks for help in advance.