Hello everyone, I'm new and need some help

I've been struggling two questions for like two hours already. Sorry in advance if this sounds unclear, english isn't my native language and I'm not sure of the english names for what I refer to -

1) I have a collection of complex numbers vectors in C^3.

I need to find if they're independent when C^3 is linear map over C, and same if C^3 is linear map over R.

What is the difference in dependency if C^3 is over C or over R? The question is not if they're a linear map so the field, be it C or R, has no meaning, no? :S I don't understand it.

2) Need to solve the following equation:

z^4 = (-\sqrt(3) + i ) / ( -1 - i * \sqrt(3) )

I'll start by saying that I spend too much time doing it all over and over again. I'm not even sure how is this supposed to look :S

Is it

z^4 = ( \sqrt(3)*i^2 + 4i + \sqrt(3) )/4 ? :S

If it is, how do I go from here? What do I do?

Thanks in advance!