Two complex number problems!

Hello!

(**First problem) Express in terms of and **

**Attempt:** According to **de Moivre's formula** - so:

**de Moivre** - and

**binomial** -

So,

(1)

After some arithmetic arrangements and and **Pythagorean trigonometric identity** I got this: and task under a) is completed (I think).

But the problem is at task b), so, I don't know how to write expression (1) in terms of cosx function. Is there any identity? Or maybe some other method.

(**Second problem) If is a complex number, what does this equation represent: **

**Attempt:** No attempt. I need a complete solution and explanation.

Thank you!