Question

Post an an example of a set of conjugates (they contain either a radical or be complex numbers). Show the result of the product of your conjugates.

Answer 1

\[z=12-\sqrt 5\\
\bar z = 12+\sqrt 5\]
\[z\bar z=(12-\sqrt 5)(12+\sqrt 5)\\\quad =12^2+12\sqrt 5-12\sqrt 5-\sqrt 5^2\\\quad = 12^2-5\\\quad = 144-5\\\quad = 139\]