1. Section 3.2 Complex Numbers
Honors Algebra 2
Section 3.2
Complex Numbers

3. Do you remember when you were told there was no Santa Claus?

4. When you learned about real numbers, you probably assumed that’s ALL numbers
There is a bigger world of numbers out there!!

5. Complex numbers includes the set of real numbers and the set of imaginary numbers

6. The standard form of a complex number is
𝒂+𝒃𝒊
When b=0, the number is real
When a=0, the number is pure imaginary
Think of these as
purebreds

7. The equation 𝑥 2 =−4 has no real solutions.
The solutions to this equation are imaginary.
Imaginary unit-(i) the square root of -1 ( −1 )
𝑖 2 =−1
i can be used to find the square root of a negative number

8. All other complex numbers have a real part and an imaginary part
Think of them as mutts

9. To simplify a pure complex number, take any perfect square factors and -1 out of the radical −75 −1∙25∙3 5𝑖 3 Try these: 1. −36 2. − −8 4. −27

10. Equal complex numbers
If 5+𝑥𝑖=𝑦−2𝑖, what do you think x and y are equal to?

11. Adding and subtracting complex numbers is easy!
Add or subtract the “a” terms
Add or subtract the “b” terms
Simplify the following:
(6−2𝑖) +(11+8𝑖)
−𝑖 −(3+5𝑖)

12. When multiplying complex numbers:
(You already know how to multiply to real numbers)
Real times imaginary
One term x two terms- use distributive prop.
Two terms x two terms- use FOIL

13. Write answers in the form 𝑎+𝑏𝑖
Never leave 𝑖 2 in your final answer!
Try these:
1. 5𝑖(8−3𝑖)
𝑖 6−7𝑖
3. (3+𝑖)(4−𝑖)

14. Solving quadratic equations when b=0
Isolate the variable
Take the square root of each side. Don’t forget ±.
Try these:
𝑥 2 =−105
2. 𝑥 2 =−45
3. 2𝑥 2 −8=−24

15. Finding Zeros of a Quadratic Function
Replace f(x) with zero
Solve
1. Find the zeros of 𝑓 𝑥 =6 𝑥 2 +42
2. Find the zeros of 𝑓 𝑥 = 2𝑥 2 +2

16. Assignment #10
Pg #1-43 odd, odd