# derive-it.com

• ## Fundamental Laws of Arithmetic

Here is a continuation of this post. Long story short, I am learning number theory from a book . The author of this book  begins his own analysis of number theory with the “system of rational numbers, i.e. of numbers integral and fractional, positive and negative, including zero.” There is a brief mention that the rational…

• ## Reaching for that Number Theory book (Part I)

I now turn to number theory, because this field seems like a solid foundation for mathematics and physics. I start with Chapter 1 of the esteemed book, Theory and Application of Infinite Series . The title of Chapter 1 is “Principles of the theory of real numbers.” Section 1 is called “The system of rational…

• ## De Moivre’s Theorem

This is a proof of de Moivre’s Theorem. This was originally presented by reference . References  https://ccrma.stanford.edu/~jos/st/Direct_Proof_De_Moivre_s.html

This post includes proofs of two angle addition identities. $\sin(x+y) = \sin x \cos y + \sin y \cos x$ $\cos(x+y) = \cos x \cos y – \sin x \sin y$   References  https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/proof-angle-addition-sine  https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:trig/x9e81a4f98389efdf:angle-addition/v/proof-angle-addition-cosine