Geometry and complex numbers.

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

displaymath11

Solution:

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

displaymath15

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

displaymath25

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]

S.O.S MATHematics home page

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

Author: Michael O'Neill

Copyright 1999-2017 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA
users online during the last hour