My answers:
u + v: H
u + w: B
v + w: D
u + v + w: E
uv: G
uw: F
vw: A
uwv: C
Working:
When trying to solve the problem, I realized that one way that I can start by approximating my values. Looking at the graph and using the unit circle on the diagram and Desmos, I came up with the following approximations:
u = (0.4, -0.3 i)
v = (0.87, 0.5 i)
w = (-2.5, 1.5 i)
I then proceeded to do the calculations and derived my answers based on the solution and the proximity of the point to the solution. Since these points are close approximations to the actual values of the points, I was not too worried if the x value I got was 1.7 and the point I chose had a x value of approximately 1.55.
I will not be uploading all the uploading addition calculations, but I will be uploading a sample of an addition calculation and my multiplication calculations.
u + w + c = 0.4 - 0.3i + 0.87 + 0.5i -2.5 + 1.5i = -1.23 + 1.7i. The most likely point is E
uw = (0.4 - 0.3i)(-2.5 + 1.5i) = -1 + 0.75i + 0.6i - 0.45i^2 = -0.55 + 1.35i. The most likely point is F.
uv = (0.4 - 0.3i)(0.87 + 0.5i) = 0.348 - 0.261i + 0.2i - 0.15i^2 = 0.348 + 0.15 - 0.061i = 0.498 - 0.06i. The most likely point is G
uwc = (0.4 - 0.3i)(0.87+0.5i)(-2.5 +1.5i) = (0.498 - 0.06i)(-2.5+1.5i) = 1.335 + 0.897i. The most likely point is C