What is the conjugate in algebra?

The conjugate can only be found for a binomial. Let a + b be a binomial. Then, the conjugate of a + b is a - b. Let a - b be a binomial, then the conjugate of a - b is a + b.

Notice that conjugates differ only in the sign of the second term. 

Number pairs of the form

a + √b and a - √b

√a + √b and √a - √b

are also called conjugates.


Binomials of the form a + bi and a - bi are called complex conjugates. 

More examples of conjugates

2 + √5 and 2 - √5

-3 + √7 and -3 - √7

√11 + √13 and √11 - √13

√5 + √3 and √5 - √3

1 - i and 1 + i

3 + 3i and 3 - 3i

The conjugate can be very useful when we are trying to simplify radical expressions or complex numbers.

Recent Articles

  1. Quadratic Formula: Easy To Follow Steps

    Jan 26, 23 11:44 AM

    Quadratic formula
    Learn about the quadratic formula, the discriminant, important definitions related to the formula, and applications.

    Read More

  2. Area Formula - List of Important Formulas

    Jan 25, 23 05:54 AM

    Frequently used area formulas
    What is the area formula for a two-dimensional figure? Here is a list of the ones that you must know!

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes