Question

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

Answer 1

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
`i` is now eliminated and we get,

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