Assertion: group's root | /r/CapableOf | come in complex conjugate pairs
Facets:
Source sentences:
text: use the primitive element theorem to write K = ℚ( α ) , and then r 1 is the number of conjugates of α that are real, 2 r 2 the number that are complex; in other words, if f is the minimal polynomial of α over ℚ , then r 1 is the number of real roots and 2r 2 is the number of non-real complex roots of f (which come in complex conjugate pairs);
text: , and then is the number of conjugates of that are real, the number that are complex; in other words, if is the minimal polynomial of over , then is the number of real roots and is the number of non-real complex roots of (which come in complex conjugate pairs); write the tensor product of fields K ⊗ ℚ ℝ as a product of fields, there being r 1 copies of ℝ and r 2 copies of ℂ .