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.

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