1. DIVIDING COMPLEX NUMBERS

2. DO NOW Today’s Objective IWBAT multiply and divide complex numbers... And Why To work with the square roots of negative numbers 3. ( 3-2i) + (-5-9i) 4. (2 - 5i) - (-1 - 6i) -2i - 8i 2 -2i -8(-1) = -2i + 8 -10 + 35i +2i -7i 2 -10 + 37i + 7 = -3 + 37i -2 -11i 3 + 1i

3. Dividing Complex Numbers When we divide, we need to find the Conjugate. The complex numbers & are called complex conjugates (They are EXACTLY the same except for the + or -)

4. TRY THESE: 1. 2.3. -6 – 5i 8 + i 9i

5. 3 - 2i3 + 2i

6. Dividing Complex Numbers To divide you must clear the denominator of all i ’ s (called “ rationalizing ” ) To rationalize, multiply the numerator and denominator by the conjugate of the denominator Quotient = Divide

7. Example 1:

8. What happens if you multiply conjugates??? Important: The product of two complex conjugates is always a real number.

9. STEP 4:

11. DIVIDE

13. Example #3 30 + 12i = 25 +10i -10i -4(-1) 2 30 + 12i = 30 + 12i 25 +4 29 = Step4. Step 3: Step 2: Step 1: Step 5: 30 + 12i 29 29

14. Example #4 Find the quotient (5+2i) and (4 - 3i) or

15. Exit ticket answer key