Hint : evaluate , where .
Sketch:
w=((i+z)/(i-z))
for:C\{z=x+iy,x≤0,y=0}
So basically for all z, ecxluding :x is less than or equal to zero and y=0.
I have solved for z which gives me:
z=((wi-i)/(w+1))
What is the easiest way to graph this? the lecturer graphed the answer but didnt really explain how to get the answer.
I know it because I've done it before! It's as simple as that.
In fact, sending the real number to is just like doing a stereographic projection of the real line to the unit circle. It's essentially the complex form of the tangent half-angle formula. You should have gotten .
Practice, my friend! I had almost the exact same question two weeks ago - I had to find the image of the first quadrant under that transformation. I could see that the real line was going to the unit circle, but not much more than that. It was the first time I ever asked for help on MHF (and I got it ).