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Complex Algebra: Trigonometry (tan)

  1. Nov 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Let tan(q) with q ε ℂ be defined as the natural extension of tan(x) for real values

    Find all the values in the complex plane for which |tan(q)| = ∞

    2. Relevant equations

    Expressing tan(q) as complex exponentials:

    (e^iq - e^(-iq))/i(e^iq + e^(-iq))

    3. The attempt at a solution

    I really have no idea how to get around this problem. No matter what I equate 'q' to I don't seem to get a valid answer. Any help would be greatly appreciated.
     
  2. jcsd
  3. Nov 25, 2012 #2

    Dick

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    tan(q) having a pole means the denominator must vanish. So you want to find values of q where e^(iq)+e^(-iq)=0. Multiply both sides by e^(iq).
     
  4. Nov 25, 2012 #3
    Ok, so I get q= ∏/2 (which makes sense since tan(∏/2)= ∞), but what does this mean exactly? Are the range of values when x + iy = ∏/2? Surely this simply leads to x = ∏/2 which is evidently not a 'range' of values. This is the simpler of problems that I need to do, though it's the one that's given me more trouble (I've got a few complex derivatives questions which were pretty straight forward to me compared to this, strangely enough)
     
  5. Nov 25, 2012 #4

    Dick

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    e^(x)=e^(x+2*i*pi*n) for any integer n. So, yes, there are lots of solutions for q.
     
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