SOLUTION: Is the product if 2 complex conjugates always a real number? Explain by using a specific example, and a general example (x's and y's).

1) Is the product of 2 complex conjugates always a real number? 

   Yes, it is.


2) Explain by using a specific example

   Specific example: 

                     Let z = 3 + 4i. 
                     Then  = 3 - 4i.
                     (3+4i)*(3-4i) =  =  = 9 - 16*(-1) = 9 + 16 = 25.


3) Explain by using a general example (x's and y's):

                     Let z = x + yi. 
                     Then  = x - yi.
                     (x+yi)*(x-yi) =  =  =  = .