1. Imaginary & Complex Numbers Obj: Simplify expressions with imaginary numbers; re-write radicals as complex expressions. Why do imaginary numbers exists and how do you add/subtract/multiply/divide imaginary numbers?

3. What do we need imaginary numbers?  Allows us to make calculations that otherwise would not be possible (ex. Electric circuits)

4. = ____________ = __________

5.  Square roots with a negative radicand should be re-written using the letter “i”  Calculator: To use the imaginary number press 2 nd, ___

6. Simplify your answers to #4 - #5 using the calculator  1.2.  3.4.

7. Re-write each radical as using the value “i”  a. b.

8. Re-write each radical as using the value “i”  c.d.

9. #1 Simplify

10. #2 Simplify

11. COMPLEX NUMBERS Real #s Ex) 2, -5, 1.3 Imaginary #s Ex) 5 i Rational Irrational Integers etc. a+bi

13. a) Simplify

14. b) Simplify

15. c) Simplify

16. d) Simplify

17. Conjugate  The opposite operation of two terms.  Ex) 5 + 2i conjugate: 5 – 2i

18.  Imaginary numbers may never be in the denominator  To eliminate them, multiply the numerator & the denominator by the conjugate

19. a)

20. b)

21. c)