1. Math is about to get imaginary!
Complex Numbers
Math is about to get imaginary!

2. Imaginary Numbers

3. Simplify imaginary numbers
Remember 28

5. Answer: -i

6. Complex Numbers: A little real, A little imaginary…
A complex number has the form a + bi, where a and b are real numbers.
a + bi
Real part
Imaginary part

7. Adding/Subtracting Complex Numbers
When adding or subtracting complex numbers, combine like terms.

8. Try these on your own

9. ANSWERS:

10. Multiplying Complex Numbers
To multiply complex numbers, you use the same procedure as multiplying polynomials.

11. Lets do another example.F O I L
Next

12. Answer:
21-i
Now try these:

13. Next

14. Answers:

15. Now it’s your turn!

16. Do Now What is an imaginary number? What is i7 equal to? Simplify:
√-32 *√2
(5 + 2i)(5 – 2i)

17. The Conjugate
Let z = a + bi be a complex number. Then, the conjugate of z is a – bi
Why are conjugates so helpful? Let’s find out!

18. We get Real Numbers!! The Conjugate = a2 + abi – abi –(bi)2
What happens when we multiply conjugates
(a + bi)(a – bi) F O I L
= a2 + abi – abi –(bi)2
= a2 – (bi)2
= a2 – b2i2 = a2 – b2(-1)
= a2 + b2
We get
Real
Numbers!!