The triangle inequality for n complex numbers.

We know the inequality when n=1 and when n=2 by the last exercise. We will show that the truth of the inequality for n=k implies it for n=k+1 when k is any integer. That will finish the proof. This is an example of proof by induction.

By the triangle inequality (in the simplest case n=2),


So the inductive hypothesis that




which is the triangle inequality for the case n= k+1.

[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 1999-2019 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