1. Section 2.2
The Complex Numbers

2. Imaginary Numbers
Invented in order to find the square root of a negative number.
Imaginary numbers are numbers that can be written using i.

3. Imaginary Numbers By definition the following new number was created:
Imaginary Unit
Which means. . .

4. Square Root of Negative Number
Caution: This rule should be used before applying any other rules for radicals.

5. Complex Number System
Mathematicians invented the complex number system in order to make it possible to solve all quadratic equations.
What is a complex number?
A real number plus an imaginary number

6. Complex Number- is an expression of the form a + bi where a and b are real numbers and
2 parts of the definition
a + bi 1. 2.
By definition . . .
Real Part
Imaginary Part
Standard Form

7. Adding/Subtracting Complex Numbers
** Procedure is the same as adding
and subtracting like terms **
ex. 3x + 5x ex w – 12 – 4w
8x w
To Add/Subtract Complex Numbers
1. Add/Subtract the real parts and add/subtract imaginary parts

8. Multiplying and Dividing Square Roots
Rule when a and b are positive . . .

9. Multiplying and Dividing Square Roots
This rule DOES NOT apply for negative numbers.
NO. . . NO. . . NO. . . NO!

10. Multiplication of Complex Numbers
Use FOIL (like multiplying binomials)
Remember . . .

12. Dividing Complex Numbers
Complex Conjugate- Conjugate of
the divisor is used to find the
quotient of two complex numbers in
standard form.
Conjugate of a+bi is a-bi
Conjugate of i is -i