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).

Question 1007085: 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).
Answer by ikleyn(52793) (Show Source): You can put this solution on YOUR website!
.

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) =  =  =  = .

RELATED QUESTIONS
Are these statements always, sometimes, or never true? If never, what is a... (answered by Theo)

1. How many solutions exist for a quadratic equation? Explain and example 2. How do we... (answered by Fombitz)

Which of the following statments are always true? (1) The sum of two imaginary numbers... (answered by rapaljer,Alan3354)

If a and b are real numbers, then the product of a+bi and a-bi is (1) always imaginary... (answered by stanbon)

What is the counter example of "The product of a number (n-1) and number (n+1) is always... (answered by jim_thompson5910)

Demonstrate, using a counter example, that the product of two isometries P and Q is not... (answered by ikleyn)

1. If a and b are real numbers, then the product of a+bi and a-bi is (1) Always... (answered by rapaljer,Alan3354,jsmallt9)

What is the solution of 5 = 17x^2 - 200x ? A. 1 real number B. 2 complex numbers that... (answered by TimothyLamb,Alan3354,reviewermath)