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.

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

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

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 ……………

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………

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

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

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