1. 5.6 – Complex Numbers

2. What is a Complex Number???
A complex number is made up of two parts – a real number and an imaginary number.
Imaginary numbers are defined to be the square root of -1
a bi
Real Part Imaginary Part

3. COMPLEX NUMBERS
Main Rules
Where i is imaginary
Examples 1) 2)

4. The Complex Number Plane2i
Because a complex number is made up of a real and an imaginary value, the complex number plane is different than an xy coordinate plane. i -2 -1 1 2 -i
Say we want to know where 2 – 2i would be
-2i
We would go left or right for the real part and up or down for the imaginary part.

5. Finding Absolute Value
Ex: |3 - 4i|
The Absolute Value of a complex number is the distance away from the origin on the complex number plane.
You can find the absolute value by using the Pythagorean Theorem. In general, 5
|a + bi|=

6. Additive Inverses of Complex Numbers
Remember that to get the additive inverse of something, you simply multiply everything by a negative
Ex: The additive Inverse of -5 is 5
Therefore, what is the additive inverse of 5 – 2i?
-5 + 2i

7. Complex Number Operations
Combining like terms (adding or subtracting)
(5 + 7i) + (-2 + 6i)
(Hint: treat the imaginary i like a variable)
3 + 13i
Multiplying Complex Numbers
(12i)(7i)
84 i2 =
84 (-1) =
-84

8. You can even FOIL Complex Numbers!
(6 – 5i)(4 – 3i) =
24 – 20i -18i + 15i2
24 – 38i + 15(-1)
24 – 15 – 38i
9 – 38i
Now, try a couple on your own:
A) (2 + 3i)(-3 + 5i)
B) (4 – 9i)(4 + 3i)
-21 + i
43 – 24i

9. SOLVING EQUATIONS WITH COMPLEX SOLUTIONS