1. I am still not very familiar and comfortable with using omega (the primitive cube root as defined in the book) to express the multiplicative inverse (like in homework 1.5, I still couldn't think of ways to express 1/(p+qa+ra^2) in the x+ya+za^2 form)
The Cardano's Formula part is a bit difficult to follow.
2. A side question that comes to me while reading page 5: do theoretical Mathematicians (as opposed to Applied Mathematicians that study Math problems with rather immediate practical usage) makes significantly less than Applied Mathematicians?
Also, the existence of Complex number has made much more sense to me when the book explain it from the prospective of the need of solving more and more difficult polynomial equations, how we expanded from N to Z to Q, R and eventually C so that we can expressed the roots of the polynomials. I am interested to know if there's a set bigger than C that is required to solve some equations.
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