In my linear algebra course, we defined the positive definite of the inner product where $<z,z> \:\ge 0$$\langle z,z\rangle \ge 0$. My professor stated that because of this $<z,z> \notin\mathbb{C}$$\langle z,z\rangle \notin\mathbb{C}$?
What is the definition of a positive so that they do not exist for complex numbers? Could you not simply form a definition of magnitude? Why is this definition not useful so that the value of the inner product is restricted to $\mathbb{R}$?
