Division of Complex Numbers
A division problem is usually given in fraction
form. To solve a division problem, we will need to know the conjugate of the denominator. The conjugate is simply the same numbers of the complex number
but with a different sign between them. For example, the conjugate of
. The terms are the same but with a different sign. Notice what will happen if you multiply the original number and its conjugate together.
In general we say:
How will this help us with a division problem? If we multiply the denominator by its conjugate, we will obtain a real number in the denominator. However, we can’t just multiply the denominator by the conjugate because it will eliminate an imaginary number
in the denominator. Whatever we do to the denominator, we must also do to the numerator. So we will multiply both the numerator and denominator by the conjugate of the denominator to solve a division problem and write our answer in standard form (
As an example of the steps needed to complete a division problem involving complex numbers, we will simplify .
- Multiply both the numerator and the denominator by the conjugate of the denominator.
- Simplify the terms.
- Written in standard form the solution is: