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. Hourly to Salary Calculator - Convert Hourly Wage to a Salary

    Jan 20, 20 05:26 PM

    Hourly to salary calculator- Convert your income to a yearly salary or a monthly salary

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

                                 Follow me on Pinterest

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.