Question 1007085
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1) Is the product of 2 complex conjugates always a real number? 

   Yes, it is.


2) Explain by using a specific example

   <U>Specific example</U>: 

                     Let z = 3 + 4i. 
                     Then {{{z[conjugated]}}} = 3 - 4i.
                     (3+4i)*(3-4i) = {{{3*3 + cross(3*4*i) - cross(3*4*i) - 4i*4i}}} = {{{9 - 16*(i^2)}}} = 9 - 16*(-1) = 9 + 16 = 25.


3) <U>Explain by using a general example (x's and y's)</U>:

                     Let z = x + yi. 
                     Then {{{z[conjugated]}}} = x - yi.
                     (x+yi)*(x-yi) = {{{x*x + cross(x*y*i) - cross(x*y*i) - yi*yi}}} = {{{x^2 - y^2*(i^2)}}} = {{{x^2 - y^2*(-1)}}} = {{{x^2 + y^2}}}.
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