1. Unit 11 Math-2 (Honors) 11.1: Dividing Square root numbers
Dividing Complex numbers and
and Graphing in the complex plane

2. Review (simplify)

3. Dividing complex numbers
NOT allowed to have
imaginary numbers
in the denominator!
Identity property of multiplication
simplify

4. Dividing square root numbers
NOT allowed to have
Square root numbers
in the denominator!
Identity property of multiplication
simplify

5. Dividing complex numbers
NOT allowed to have
imaginary numbers
in the denominator!
Identity property of multiplication
simplify
Standard form of
a complex number

6. Your turn divide (really means simplify)1. 2.

7. Multiply complex conjugates
Complex conjugate pairs
Multiply complex conjugate pairs and the
“i” term disappears!!!!

8. Dividing Complex Numbers
NOT allowed to have
imaginary numbers
in the denominator!
Multiply by “1”
(Ratio of
Complex
conjugate)

10. What about square root numbers
Multiply complex conjugate pairs and the
“ ” term disappears!!!!

11. Your Turn simplify 3.

12. Your Turn simplify 4.

13. Your Turn simplify 5.

14. The “Real” Plane y = x + 1 rule f(x) x x + 1 2 3 -1 -2 -3 1 -4 2 + 1 3
2 + 1 3
3 + 1 4
- x
+ x
-1 + 1
-2 + 1 -1
-3 + 1 -2
1 + 1 2
-4 + 1 -3
- y
0 + 1 1

15. 2 + 3i
(2, 3i)

16. We call this vector: “Z”
z = 2 + 3i
The red arrow is called a “vector” (it goes from the origin directly to the point)
We call this vector: “Z”

17. Your turn: 5.
Graph (-3 + 4i) on the complex plane (draw the vector also)
Graph (5 – 2i) on the complex plane (draw the vector also) 6.
-3 + 4i
+ real
+ imaginary
- imaginary
- real
5 – 2i

18. Now watch this: Make a parallelogram What is this complex number?
(-3 + 4i) + (5 – 2i) = ?
-3 + 4i
+ real
+ imaginary
- imaginary
- real
5 – 2i

19. Vectors are added “head to tail”
(-3 + 4i) + (5 – 2i) = ?
-3 + 4i
+ real
+ imaginary
- imaginary
- real
5 – 2i

20. Add and Then Graph the following7.
(2 – 3i) + (2 + 3i) 8.
(-3 + 4i) + (-3 – 4i)

21. Graph the two complex numbers9.
(2 –i)
+ real
+ imaginary
- imaginary
- real
10.
(2 + i)
2 + i
2 –i

22. Multiply the two complex numbers
11.
(2 –i)
(2 + i)
+ real
+ imaginary
- imaginary
- real
(4 + 1) = 5
2 + i
12. Graph the result.
5 + 0i
2 – i