Why does multiplying a + bi by the complex conjugate a -bi eliminate I from the expression

Question

asked May 21, 2019 234k views

1 Answer

Dolkar · Answer 1 · 2019-05-25T20:14:07+0000

Step-by-step explanation

The reason is that

i^2=-1

If we multiply
a+bi by its conjugate
a-bi

We obtain;

(a+bi)(a-bi)

This is difference of two squares so we obtain;

(a+bi)(a-bi)=a^2-(bi)^2

This further gives us,

(a+bi)(a-bi)=a^2-b^2i^2

Since the
i^2=-1 , we substite to get;

(a+bi)(a-bi)=a^2-b^2(-1)

The
is now eliminated and we get,

(a+bi)(a-bi)=a^2+b^2