A conjugate is formed by changing the operation between two terms in a binomial algebraic expression. Conjugates are commonly used to rationalize the denominator.
\((a+b)\) has a conjugate of \((a-b)\)
\((a-b)\) has a conjugate of \((a+b)\)
Lesson
VIDEO
Problems & Videos
\(\textbf{1)}\) Find the conjugate of \(4+\sqrt{2}\) The conjugate is \(4-\sqrt{2}\)
\(\textbf{2)}\) Find the conjugate of \(3+i\) The conjugate is \(3-i\)
\(\textbf{3)}\) Find the conjugate of \(5-i\) The conjugate is \(5+i\)
\(\textbf{4)}\) Simplify \(\displaystyle\frac{5}{3+\sqrt{3}}\) The answer is \(\displaystyle\frac{15-5\sqrt{3}}{6}\)
\(\textbf{5)}\) Simplify \(\displaystyle\frac{\sqrt{2}}{\sqrt{5}-1}\) The answer is \(\displaystyle \frac{\sqrt{10}+\sqrt{2}}{4}\)
\(\textbf{6)}\) Simplify \(\displaystyle\frac{2+\sqrt{2}}{3-\sqrt{2}}\) The answer is \(\displaystyle \frac{8+5\sqrt{2}}{7}\)
\(\textbf{7)}\) Simplify \( \displaystyle\frac{2i}{3+4i} \) The answer is \( \displaystyle\frac{6i+8}{25} \)
\(\textbf{8)}\) Simplify \( \displaystyle\frac{6+i}{3+2i} \) The answer is \( \displaystyle\frac{20-9i}{13} \)
\(\textbf{9)}\) Simplify \( \displaystyle\frac{3-2i}{4i} \) The answer is \( \displaystyle\frac{-(3i+2)}{4} \)
\(\textbf{10)}\) Simplify \( \displaystyle\frac{3}{i} \) The answer is \( -3i \)
