1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Complex Variables

  1. Sep 25, 2007 #1
    I can't think of how to title the problem I'm having, but this is what the course is called. Complex being imaginary numbers, ie z = a + ic where i is the sqrt of -1.

    So here is the question that I have no idea where to start with:

    Construct a sequence {zn} which is bounded and for which the successive
    terms get increasingly closer, but which is not convergent. In other words,
    {zn} must satisfy:
    (i) For some B > 0, |zn| < B for every n = 1, 2,...
    (ii) For every n, |zn+2 - zn+1| < |zn+1 - zn|.
    (iii) {zn} diverges.
    Note that the inequality in (ii) is strict. Make sure to prove that your
    sequence satisfies all three parts.

    n is a subscript of z.

    Thanks in advance.
  2. jcsd
  3. Sep 25, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    Let tn=sum(1/i) for i=1 to n. Consider zn=exp(i*tn). Now you just have to do the proofs.
  4. Sep 26, 2007 #3
    Thanks. On the same homework assignment, I have another problem but this is more with the question itself. What does this mean: limit of Arg z, as z approaches zero?
  5. Sep 26, 2007 #4


    User Avatar
    Science Advisor

    ?? Just what it says! Or is the question rather "what does Arg z mean"?

    Any complex number z= x+ iy can be written in polar form: [itex]z= r (cos(\theta)+ i sin(\theta)[/itex] or simply as [itex]z= r e^{i\theta}[/itex]. In either case [itex]Arg z= \theta[/itex].

    Take a look at z= x+ ix. What is Arg z for all x? What is its limit as z (and so x) goes to 0?
    Now look at z= x- ix. What is Arg z for all x? What is its limit as z (and so x) goes to 0?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook