Question

Question #8791e

Answer 1

Multiplying by the Complex Conjugate is used when you are dividing complex numbers. For instance:

`(3i+2)/(8i-11)`

In this instance, we would want to multiply by the complex conjugate, where the sign on the `i` term changes. Our new problem would be:

`(3i+2)/(8i-11)*(-8i-11)/(-8i-11)`

In short, complex conjugates are used when we're dividing complex numbers. This is mainly in precalculus.

People tend to not like irrational numbers in the denominator, so to get rid of this, we "rationalize the denominator". Here's a basic example:

`11/sqrt2`

Square roots of non-perfect squares are irrational numbers. To rationalize the denominator, we would multiply the numerator and denominator by `sqrt2`. Solution process below:

`11/sqrt2*sqrt2/sqrt2=(11sqrt2)/2`

This is used whenever there's an irrational number in the denominator.