Multiplying and Dividing Complex Numbers
Multiplying two complex numbers is accomplished in a manner similar to multiplying two binomials. You can use the FOIL process of multiplication, distributive multiplication, or your personal favorite means of multiplication.
The conjugate of a complex number a + bi is the complex number a – bi.
For example, the conjugate of 4 + 2i is 4 – 2i.
(Notice that only the sign of the bi term is changed.)
When dividing two complex numbers,
1. write the problem in fractional form,
2. rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator.
(Remember that a complex number times its conjugate will give a real number.
This process will remove the i from the denominator.)