Transcript How do we divide complex numbers?

How do we divide complex
numbers?
Do Now: What is the conjugate?
Explain why do we multiply a
complex number and its conjugate
Now that we can multiply, we
can divide!
 When multiplying or dividing, we need
to make sure that we simplify any
radicals or imaginary numbers.
 If we divide by a complex number, then
we automatically have a conflict: WE
CAN NOT HAVE AN IMAGINARY
NUMBER IN THE DENOMINATOR!!
Rationalizing




Once again we need to rationalize
We need to find our creative name for one.
Before we used the denominator as our key.
Ex.
3
2
6
6



2
2
2
4
Multiply by the conjugate
 To rationalize the denominator, we multiply by
the conjugate to create a real number.
 Ex.
5  3i 2  7i 10  6i  35i  21i 2


2  7i 2  7i
4  49i 2
10  41i  21 11 41i
11 41


  i
4  (49)
53
53 53
Example
2  3
3  3
Try on your own
2i
3 i