This document discusses graphing complex numbers and completing the square. It explains that to graph a complex number a + bi, you plot the real number a on the real axis and the imaginary number b on the imaginary axis. It also outlines the steps to complete the square of a quadratic equation: find the constant term c, add c to both sides, factor the left side, and take the square root of both sides to solve for x.

1. Graphing Complex Numbers
Algebra 2
5.4 Part 3
p. 273

2. Graphing Complex Numbers
• Real axis

3. Graphing Complex Numbers
• Real axis
• Complex or
Imaginary axis

4. Graphing Complex Numbers
• To graph the
number a + bi

5. Graphing Complex Numbers
• To graph the
number a + bi
• Go to a on the Real
axis.

6. Graphing Complex Numbers
• To graph the
number a + bi
• Go to a on the Real
axis.
• Go to b on the
Imaginary axis.

7. Graphing Complex Numbers
• For example: graph
2 - 3i.
• Out 2

8. Graphing Complex Numbers
• For example: graph
2 - 3i.
• Out 2
• Down 3

9. Graphing Complex Numbers
• For example: graph
2 - 3i.
• Out 2
• Down 3
2 - 3i

10. Complex Numbers
• The absolute value of a complex
number is the distance from the origin.

11. Completing the Square
Algebra 2
5.5
p. 282

12. Binomial Theorem
a2
+ 2ab + b2
= (a + b)2

13. Binomial Theorem
a2
+ 2ab + b2
= (a + b)2
I.e., x2
+ 4x + 4 = (x + 2)2

14. x2
- 7x + c
c = (b
/2)2

15. x2
- 7x + c
c = (b
/2)2
• What is b? -7
[remember ax2
+ bx + c?]

16. x2
- 7x + c
c = (-7
/2)2

17. x2
- 7x + c
c = (-7
/2)2
= 49
/4
• Square the top, square the bottom

18. x2
- 7x + 49
/4
Can we factor this?

19. x2
- 7x + 49
/4
= (x - 49
/4)2

20. Completing the Square
• Move the constant term to the opposite
side of the equal sign of the x-terms.

21. Completing the Square
• Move the constant term to the opposite
side of the equal sign of the x-terms.
• Find c.
• Add c to both sides of the equal sign.

22. Completing the Square
• Move the constant term to the opposite
side of the equal sign of the x-terms.
• Find c.
• Add c to both sides of the equal sign.
• Factor the left side.
• Take the square root of both sides.

23. Completing the Square
• Move the constant term to the opposite
side of the equal sign of the x-terms.
• Find c.
• Add c to both sides of the equal sign.
• Factor the left side.
• Take the square root of both sides.
• Solve for x and simplify.