2. How do we determine absolute value of complex numbers? Do Now: Explain “absolute value.” What is the distance formula? Do Now: Explain “absolute value.” What is the distance formula?

3. 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. / 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.

4. 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?

5. Magnitude / What if we were to treat the vector as a hypotenuse? / Then we could use the Pythagorean Theorem

6. / 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. / h 2 = leg 2 + leg 2

7. Example: / Ex.

8. 3+4i

9. 2–4i

10. 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. / 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.

11. Summary/HW / How is this formula similar to the distance formula and the Pythagorean Theorem? / Pg 71, all / How is this formula similar to the distance formula and the Pythagorean Theorem? / Pg 71, all