What Are the Embeddings of K in C?

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Let K=Q(i,(1+i)^(1/3)).
Describe all of K's embeddings in C.
(C-Complex Field, Q-Rational Field).

Describe? Could it be the answer is just the identity? How could I prove that?

Thanks in advance! :smile:
 
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i must go to some element that squares to 1, and 1 must go to 1, so how many choices can that be?
 
Good point, stupid me.
(You meant -1 I suppose).

So actually, it is true that for Q, the only embedding is id?
(1 must go to 1, therefore N - Natural numbers - must go to N, and therefore Q must go to Q)

And in this case, I have like... 6 choices or so? (i goes to i or -i, plus playing with the cubic root a little bit)

I'm going to go try and formalize it. I'll come back if I have any prob.
Thanks a lot!

Oh, and if I wrote sth. stupid, feel free to throw it in my face. :biggrin:
 

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