EXPLANATION
The reason is that
[tex]i^2=-1[/tex]
If we multiply [tex]a+bi[/tex] by its conjugate [tex]a-bi[/tex]
We obtain;
[tex](a+bi)(a-bi)[/tex]
This is difference of two squares so we obtain;
[tex](a+bi)(a-bi)=a^2-(bi)^2[/tex]
This further gives us,
[tex](a+bi)(a-bi)=a^2-b^2i^2[/tex]
Since the [tex]i^2=-1[/tex], we substite to get;
[tex](a+bi)(a-bi)=a^2-b^2(-1)[/tex]
The [tex]i[/tex] is now eliminated and we get,
[tex](a+bi)(a-bi)=a^2+b^2[/tex]
