来自《耶鲁大学开放课程：基础物理 第16集 第16集》

• 
  
  (a+b)·(a-b)=a^2+b^2
  由于 (a+b)·(a-b)=a^2+b^2
• 
  
  But remember, b is i·y
  不过记得 这里 b 是 i·y
• 
  
  So, when you take the square of that,
  当你对它求平方时
• 
  
  you should keep track of
  要注意正负号
• 
  
  all the signs and you will find it's x^2+y^2.
  最后结果为 x^2+y^2
• 
  
  We denote that as this, and this thing is called the modulus of z
  我们把这个符号定义为 z 的模
• 
  
  It's the length of the complex number z,
  根据勾股定理
• 
  
  just given by Pythagoras' theorem.
  这就是复数 z 的长度
• 
  
  You should know, whenever you take a complex number,
  要记住 对于任何一个复数
• 
  
  multiply by each conjugate, by its complex conjugate,
  乘以其共轭复数后
• 
  
  the result will be a real number equal to
  结果都是一个实数
• 
  
  the square of the length of the complex number.
  等于此复数的模的平方