9.1 # 19
I'm having trouble understanding this one. It asks you to sketch a graph of all complex numbers z that would fulfill the equation absvalue(z-1)=10. I know this is a circle with radius 10, but I'm having a hard time determining the center. The book hints that "1" corresponds to the complex point (1,0) and asks how far apart z and 1 are. I think this would mean that z is one unit to the left of z-1, but I don't know how to figure out how far apart z and (1,0) are. Basically... the book makes the circle's center (1,0) and I'm wondering if anyone understands why. I'm probably overthinking it...
posted by Casey Blue at 12:24 PM
1 Comments:
Think of it like a translation. If the center starts at (0,0) for the circle |z| then the circle |z-1| would be translated one unit to the right so that it has a center of (1,0). It says that |z-1|=10 so the radius is 10. This gives the solution in the book.
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