1. 3.2: Imaginary Numbers Objectives: • Define “imaginary” numbers
• Solve quadratic equations with
complex roots.

2. Concept: Imaginary Unit
The reason for the name “imaginary”
numbers is that when these numbers
were first proposed several hundred
years ago, people could not “imagine”
such a number.
Can you?

3. Concept: Imaginary Unit cont . . .
Imaginary numbers occur when the solution to a quadratic is not in the set of “Real” numbers. (Hence: imaginary)
Example: x2 + 2 = 1
– 2 – 2
x2 = –1
√x2 √–1
x = √–1
Note: you can not take the square root of a negative number (Go ahead, try it on your calculator.)
So, now what?
x = + i

4. Concept: Simplifying Negative Radicals

5. Concept: Simplifying Negative Radicals
Your Turn!!!
–18
–48
Now, let’s use it when solving equations. We will
do everything exactly like we did in the last lesson,
but now, we will have a solution, even when the
calculator says we don’t.
Solve for x: