Conjugate
The conjugate is where you change the sign in the middle of two terms like this:
It is only used in expressions with two terms (called "binomials")
Other examples:
| Expression | Its Conjugate |
|---|---|
| x2 - 3 | x2 + 3 |
| a + b | a - b |
| a - b3 | a + b3 |
Examples of Use
The conjugate can be very useful because ...
... when you multiply something by its conjugate you get squares like this:
How does that help?
It can help you move a square root from the bottom of a fraction to the top (or vice versa). And I will show you how.
 |
Note: The bottom of a fraction is called the denominator, and many square roots are irrational, so this is called "Rationalizing the Denominator" |
Example: here is a fraction with an "irrational denominator":
How can we move the square root of 2 to the top?
Answer! Multiply both top and bottom by the conjugate (this will not change the value of the fraction), like this:
(Did you see how the denominator became a2-b2 ?)
There is another example on the page Evaluating Limits where I move a square root from the top to the bottom.
So try to remember this little trick, it may help you solve an equation one day!