Analysis

• Oct 25th 2008, 09:23 AM
Louise
Analysis
I have been asked to give an example of a sequence in C (complex) which tends to zero but the principal value if the argument does not tend to a limit.

I know that one example would be Zn=(-1)*n/n for n>=1.

However i don't understand how the principal value alternates between pi and 0 for this example, or how to calculate the principal value for a complex sequence in general.

Any help wold be greatly appreciated. Thanks.
• Oct 25th 2008, 09:29 AM
Plato
If you mean $z_n = \frac{{\left( { - 1} \right)^n }}{n}$, then yes that works,
• Oct 25th 2008, 09:36 AM
Louise
Can you please explain how to calculate the principal value of the argument of this example.

Also, how do i find other examples?
• Oct 25th 2008, 09:43 AM
Plato
$Arg\left( {z_n } \right) = \left\{ {\begin{array}{rl}
0, & {\mbox{n is even}} \\
\pi , & {\mbox{n is odd}} \\ \end{array} } \right.$