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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