Question

Points z1 and z2 are shown on the graph. (10 points)

complex plane, point z sub 1 at 4 to the right of the origin and 6 units up, point z sub 2 at 5 units to the left of the origin and 2 units up

Part A: Identify the points in standard form and find the distance between them.

Part B: Give the complex conjugate of z2 and explain how to find it geometrically.

Part C: Find z2 − z1 geometrically and explain your steps.

Answer 1

Part A: The point z1 is at (4, 6) and the point z2 is at (-5, 2). The distance between them is √((4-(-5))^2 + (6-2)^2) = √(9^2 + 4^2) = √(81 + 16) = √97.

Part B: The complex conjugate of z2 is (-5, -2). Geometrically, it can be found by reflecting the point z2 across the x-axis.

Part C: To find z2 − z1 geometrically, you can draw a vector from z1 to z2. The coordinates of this vector are (-5-4, 2-6) = (-9, -4). So z2 − z1 = -9 - 4i.