Page 287 ch 3.4 Complex Zeros and the Fundamental Theorem of Algebra. A conjugates question.
I am confused with the last paragraph on page 288 of the 3rd corrected edition of College Algebra.
The paragraph states (with __ for the top bar since I can't type this): "The notation commonly used for conjugation is a 'bar': __a+bi__ = a-bi. For example, __3+2i__ = 3 - 2i, __3-2i__ = 3 + 2i, __6__ = 6,
__4i__ = -4i, and __3 + sqrt(5)__ = 3 + sqrt(5).
__3 + sqrt(5)__ = 3 + sqrt(5)
I am confused as to why it is + on both sides versus +/-. Is it because 3 + sqrt(5) is a real number when evaluated, and thus it is in actuality the real part of a complex number, thus it is similar to _6_= 6? I am confused because when rationalizing the denominator with square roots, from what I recall, the conjugate would be _3 + sqrt(5)_ = 3 + sqrt(5). Is there a difference in syntax and semantics between complex conjugates versus conjugates containing only real numbers and radicals?