Math 210-01: Linear Algebra: Reading Homework 8.3--8.4

1. Polar Form and DeMoivre : what basic procedure(s) are facilitated by the polar form of a complex number?
   
   1. Polar Form : what is polar form of a complex number?
      
      1. argument : what is the principal argument of a complex number? why do we need to define it? how is it denoted?
         
   2. DeMoivre's Theorem : what is DeMoivre's theorem?
      
      1. nth roots : how is the nth root, w, of a complex number z defined?
         
      2. finding nth roots : how do we calculate the nth root of a complex number?
         
      3. nth roots of unity : what are the nth roots of unity?
         
2. Complex Vector Spaces and Inner Products : what is a complex vector space?
   
   1. $C^n$ : what is $C^n$? what is a standard basis for it? what is its dimension?
      
   2. Inner products : what is the Euclidean inner product?
      
      1. properties : what properties does the Euclidean inner product have?
         
      2. norms : what is the Euclidean norm? Euclidean distance?
         
   3. Complex Inner Products : how is a complex inner product defined?