I have answered the question by dividing it up into two sections, the sums (the first four expressions) and the products (the last four expressions).
To answer the first section, I used the "parallelogram" method. This method uses the fact that the addition of complex numbers on an Argand diagram essentially uses the same idea of the addition of vectors. I drew lines from the origin to u, v, and w (as shown in the image), these would act as the sides of the parallelogram that I will be making.
For the ease of explanation, suppose u = a-bi, v = c+di, and w = -e+fi where a, b, c, d, e, and f are constants, e>c>a, and f>d>b
u+v = h, I drag the line u and place its end-point on point v, this line must be downward sloping from point v since we are adding the real values but subtracting the imaginary ones.
When we add the two complex numbers, the sum is as follows:
(a-bi)+(c+di) = a+c+i(-b+d)
Since a and c are added up, we know that the real value will be positive and since d>b, the difference of the imaginary values will be positive but lower than b (which is why the line u must be downward sloping from point v), thus showing that the value will be in the first quadrant.
u+w = b,
(a-bi)+(-e+fi) = a-e + i(-b+f)
Since e>a and f>b, we can deduce that the answer is in the second quadrant and the imaginary component < f and the real component > -e (resultant point will be below and on the right side of w), which means it is either b, c, or f. We also now know that the origin point on line u will be shifted to point w on the line w, doing so shows that the sum of the complex numbers add up to b.
v+w = d,
(c+di)+(-e+fi) = c-e + i(d+f)
The real component is going to be negative since e>c and be on the right side of w since it is the difference of the two real values, and the imaginary component will be positive and above w since d and f are being added. Therefore, the points must b, d, or e. Placing the origin point of live v on the point w shows that the answer is d.
u+v+w = e,
(a-bi)+(c+di)+(-e+fi)= a+c-e + i(-b+d+f)
The real component will be negative since e>(a+c). This is proven by using the parallelogram rule. It is even safe to assign estimated values to a, c and e in this question, let 1>c>1/2 and 0<a<1/2, and 2.5>e>2, these estimations have been made assuming that every point on the axis =1/2 since the radius of the circle=1 and that is the second point on either axis. So let a and c =1/2 -a wild guess but close enough to prove what we need to, 1/2 + 1/2 < 5, therefore, (a+c)<e. Anyway, since e>(a+c), we know that the real value will be negative and on the right side of w. And since f>b and d>b and f and d are being added, the imaginary value has to be positive and above w. Therefore, the answer must be in the second quadrant and be either d, or e. Since d is already equal to v+w, the answer must be e.
If we were to use the parallelogram rule here, we would first find the answer of the sum of two complex number (say, v+w = d) and then place the end point of the third complex number from the new point (so the origin point on line u is placed on point d). In this question, we get to answer e.
To find the result of the last four expressions, I used the GeoGebra interactivity from the question "Into the Wilderness". I gave any random value to the complex numbers u, v, and w but made sure that the moduli of the lines were somewhat similar to the given question and the points were in the correct quadrants (eg: We know that the modulus of w is the greatest since it is outside the circle, and modulus of u is the smallest since it is inside the circle, modulus of v is between them since it is on the circle). After that, the resultant complex number was found by approximation and elimination (if required).
uv = g,
I set the radius to 1 and placed z1 where point v is on this question and z2 where point u is, the resultant complex number- z3- was inside the circle and in the fourth quadrant, the only such point in this given question is g.
vw = a,
Leaving z1 where it was, I moved z2 to point w, the resultant complex vector was very close to the real axis, in the second quadrant, and on the left side of z2, the only such point in the question is a.
At this point, the two expressions remaining are uw and uvw and the points left are f, and c. To match these expressions and points using the GeoGebra interactivity, I needed to compare the positions of the two points.
I first found the approximate position of uw, I reduced the radius and positioned z1 on point u, z2 was on point w. This gave me a point z3 which was fairly close to the imaginary axis and was in the second quadrant. I was fairly certain that the answer would be f but just to confirm I deduced uvw first.
To find uvw, I placed z1 on the resultant complex number of uw and placed z2 on v, the resultant value was lower than that of uw but still in the second quadrant. In the given question, this corresponded to point c, thus also confirming that uw = f.
So, uw = f
uvw = c
Finally, I will just list all the answers again here;
u+v = h
u+w = b
v+w = d
u+v+w = e
uv = g
uw = f
vw = a
uvw = c