Geometry and complex numbers.
Geometry and complex numbers.
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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