Graphing Complex Numbers

Algebra 2

5.4 Part 3

p. 273

Graphing Complex Numbers

• Real axis

Graphing Complex Numbers

• Real axis

• Complex or Imaginary axis

Graphing Complex Numbers

• To graph the number a + bi

Graphing Complex Numbers

• To graph the number a + bi

• Go to a on the Real axis.

Graphing Complex Numbers

• To graph the number a + bi

• Go to a on the Real axis.

• Go to b on the Imaginary axis.

Graphing Complex Numbers

• For example: graph 2 - 3i.

• Out 2

Graphing Complex Numbers

• For example: graph 2 - 3i.

• Out 2• Down 3

Graphing Complex Numbers

• For example: graph 2 - 3i.

• Out 2• Down 3

2 - 3i

Complex Numbers

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

Completing the Square

Algebra 2

5.5

p. 282

Binomial Theorem

a2 + 2ab + b2 = (a + b)2

Binomial Theorem

a2 + 2ab + b2 = (a + b)2

I.e., x2 + 4x + 4 = (x + 2)2

x2 - 7x + c

c = (b/2)2

x2 - 7x + c

c = (b/2)2

• What is b? -7[remember ax2 + bx + c?]

x2 - 7x + c

c = (-7/2)2

x2 - 7x + c

c = (-7/2)2 = 49/4

• Square the top, square the bottom

x2 - 7x + 49/4

Can we factor this?

x2 - 7x + 49/4

= (x - 49/4)2

Completing the Square

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

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.

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.

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.