Geometry and complex numbers.

Exercise: Let tex2html_wrap_inline7 and tex2html_wrap_inline9 be distinct complex numbers. Describe the set of points



First consider the case when tex2html_wrap_inline13 . Then the set in question is


Writing tex2html_wrap_inline17 for some r and tex2html_wrap_inline21 we see that the above set is simply the line segment from the origin to tex2html_wrap_inline9 .

Now we can write


and we see that our set is the line segment from the origin to tex2html_wrap_inline27 translated by tex2html_wrap_inline7 . Checking the endpoints, we see that this is the line segment joining tex2html_wrap_inline7 to tex2html_wrap_inline9 .

[Algebra] [Complex Variables]
[Geometry] [Trigonometry ]
[Calculus] [Differential Equations] [Matrix Algebra]

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Author: Michael O'Neill

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