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.

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.