Step 1.  Multiply (a+bi) by (c+di);  then take the bar over this product.

         it will be (z* w) bar.



Step 2.  Take bars first, transforming  a+bi  to  a-bi
                          and           c+di  to  c-di.

         Now multiply  (a-bi)  by  (c-di).

         It will be z bar * w bar.



Step 3.  Now compare your results in steps 1 and 2.

         If you calculated everything correct, you must get identical results,
         which will prove your statement.

         It you will get different results,  then check and re-check, double check and cross-check,
         until you find and correct all possible mistakes.