1. L4 distance in the complex plane
N-CN.6 Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers and its endpoints.

2. Warm up
Find the distance and midpoint of the line segment with the given endpoints.
1. (4, 4) , (– 1, 2)
2. (6, 2), (2, –3)
3. (0, 0), (0, 10)
4. (–5, 3), (–3, –3)
5. addition and subtraction on vectors

3. distance between numbers in the complex plane
Plot these 2 complex numbers on a complex plane z = 2 + 3i and w = – 5 – i

4. Find the distance between point z and w
Use pythagorean theorem,
horizontal distance from w to r is …………
Vertical distance from w to r is …………
The distance from w to r is ……………

5. Find the distance between point z and w
Use pythagorean theorem,
horizontal distance from w to r is ……7……
Vertical distance from w to r is ……4……
The distance from w to r is ……sqr 65………

6. Find the midpoint of 2 complex numbers
z = 2 + 3i and w = – 5 – i
Use the midpoint formula to find the midpoint.

7. A4. Plot w, z, w + z, and w – z in the complex plane.
1. w = 1 – i. z = 4
2. w = –2 – 3i. z = –2 + 3i
3. w = 3 + i. z = 3 – i
4. w = 2i. z = 2 + i
5. w = 4 – 3i. z = –2 + 5i

8. Reflections