By the definition of "complement" of a complex number.
If x= a+ bi, then .
If particular, if x= a+ bi and y= c+ di, then x+ y= (a+ c)+ (b+ d)i so and xy= (ac- bd)+ (ad+ bc)i so [tex]\overline(xy)= (ac-bd)- (ad+ bc)i= (a- bi)(c- di)= \overline{xy}[/itex].