Exercise: Let and be distinct complex numbers. Describe the set of points
Solution:
First consider the case when . Then the set in question is
Writing for some r and we see that the above set is simply the line segment from the origin to .
Now we can write
and we see that our set is the line segment from the origin to translated by . Checking the endpoints, we see that this is the line segment joining to .
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Author: Michael O'Neill