Show that the galois group for (Complex : Reals) is given by {e, y} where y is y: C-->C is the conjugation automorphism defined by y(z) = z~ (Conjugate of z) for all z in C.(adsbygoogle = window.adsbygoogle || []).push({});

if o is an element of gal(C:R) and z = a + bi in C, then o(z) = o(a+bi) = o(a)+o(b)o(i) = a+bo(i)

but o(i)^2 = o(i^2) = o(-1) = -1, so o(i) = i or o(i) = -1.

I am confused on why o(i) can ever equal i... isn't the conjugate of i going to be -1 every time?

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# Trouble understanding simple Galois Theory example

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