Complex Numbers: Conjugates

The complex conjugate of a number is quite similar to the conjugate of a binomial. Let us say a complex number is written in the form $a+bi$. Now, the conjugate would be $a-bi$. This can be very useful for "rationalizing" the denominator. If you want to simplify $\frac{1+i}{1-i}$, you would multiply both the numerator and denominator by the conjugate of $1-i$, which is $1+i$.