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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.