1. Complex Numbers and Roots
5-4
Complex Numbers and Roots
SWBAT:
Define and use imaginary and complex numbers.
Solve quadratic equations with complex roots.
Holt Algebra 2

3. Square Roots:
Let’s Review some properties of roots

4. You can see in the graph of f(x) = x2 + 1 below that f has no real zeros. If you solve the corresponding equation 0 = x2 + 1, you find that x = ,which has no real solutions.
However, you can find solutions if you define the square root of negative numbers, which is why imaginary numbers were invented. The imaginary unit i is defined as You can use the imaginary unit to write the square root of any negative number.

5. Imaginary Numbers: So far we have used real numbers.
Now we use imaginary numbers: ‘i’
i =
i2 = -1
Ex: = 4i

6. Simplifying Square Roots of Negative Numbers
Express the number in terms of i.

7. Solving a Quadratic Equation with Imaginary Solutions
Solve the equation.
5x = 0
x2 = –36
x = 0
9x = 0

8. Homework
2. Pg 264 #26-29, #42-45 all