1. Bell Ringer

2. Complex Numbers Friday, February 26, 2016

3. What is i?  Until this point, you have been told you cannot take the square root of a negative number… because it isn’t real.

4. What is i 2 ?

5. More about i  Figure it out.  Is there a pattern?

6. Since the powers of i repeat every 4 th time…  Divide the exponent by 4.  If the decimal part of your answer is: .25 = i .5 = -1 .75 = -i  0 = 1  i 99 = ?  99 / 4 = 24.75  Therefore, i 99 = -i

7. Adding & Subtracting  Add: Just like with polynomials, you combine like terms.  Subtract : Just like with polynomials, you add the opposite.  (6 + 5i) + (-2 + 3i)  4 + 8i  (6 + 5i) – (-2 + 3i)  6 + 5i + 2 – 3i  8 + 2i

8. Multiplying  Just like polynomials, distribute or box it!  (6 + 5i) (-2 + 3i)  -12 + 18i – 10i + 15i 2  -12 + 8i + 15i 2 But Wait…..

9. What is i 2 ?  So looking at our problem:  -12 + 8i + 15i 2  We can simplify farther.  -12 + 8i + (15)(-1)  -12 + 8i – 15  -27 + 8i

10. Order is Important!  We write complex numbers with the “real” part first, followed by the “imaginary” part.  So it’s a + bi  So, it’s -27 + 8i  Not 8i - 27

11. Time to Practice!  Classwork: Odd #s Complex Numbers Homework: Even #s Complex Numbers

12. Exit Ticket  What is the pattern for i?  How can you calculate in the complex number system on your calculator?