How do we determine absolute value of complex numbers?

1
How do we determine absolute value of complex
numbers?

• Do Now Explain absolute value.
• What is the distance formula?

2
Absolute value

• The distance from the origin is absolute value.
• Five is located 5 units from the origin, so the
  absolute value is 5.
• Negative five is also located 5 units from the
  origin, so the absolute value is also 5.
• Absolute value is always positive.

3
How does this relate to complex numbers?

• Remember, we can plot complex numbers on a
  coordinate grid
• We need to measure from zero to the point.
• What is the magnitude of the vector?

4
Magnitude

• What if we were to treat the vector as a
  hypotenuse?
• Then we could use the Pythagorean Theorem

5

• The length of the blue line can be found by
  finding the sum of the squares of the vertical
  line and the horizontal line, and taking the
  square root.
• h2 leg2 leg2

6
Example

• Ex.

7
34i
8
24i
9
Review

• Absolute value is distance from the origin
• The general formula to determine absolute value
  is
• There should NEVER be a minus between the two
  terms in this radical.

10
Summary/HW

• How is this formula similar to the distance
  formula and the Pythagorean Theorem?
• Pg 71, all