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

EXPLANATION

The reason is that

If we multiply by its conjugate

We obtain;

This is difference of two squares so we obtain;

This further gives us,

Since the , we substite to get;

The is now eliminated and we get,

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0