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Complex Numbers

  1. Apr 8, 2009 #1
    1. The problem statement, all variables and given/known data
    If z = x + ( x+1) i, find the value of x for which Arg (z) = pi/3


    2. Relevant equations



    3. The attempt at a solution
    ( x+1/x) = pi/3
    x = 3/( pi -3)

    Answer: ( 3) ^(1/2) + 1 divided by 2
     
  2. jcsd
  3. Apr 8, 2009 #2
    Where did you get these equations from? Remember that [itex]\arg z = \theta[/itex] is equivalent to [itex]z = |z|(\cos \theta + i \sin \theta)[/itex].
     
  4. Apr 8, 2009 #3
    I'm working out the arg of z in term of x
    tan ( y/ x) = ( x+1)/ x = pi/3
     
  5. Apr 8, 2009 #4
    I assume x is a real number, correct?

    It might help you to draw the point z in the complex plane. What is the horizontal component of z? What is the vertical component? Where is the angle arg(z)? You should have a right triangle with one of the angles equal to pi/3.

    Once you've drawn this, you can use what you know about this triangle to write the equation for x. (pi/3 rad = 30 deg, in case you forgot that.)
     
  6. Apr 8, 2009 #5
    Oops - your second post came in while I was responding.

    Be careful - arg(z) = pi/3 is the angle, so tan(y/x) = pi/3 is wrong.

    (You've just got it backwards - recall how tan() is defined and you're there.)
     
  7. Apr 8, 2009 #6
    so it's
    tan ( pi/3 ) = ( x+ 1 / x)
     
  8. Apr 8, 2009 #7
    Nope. What kind of number goes into the argument of a trig function? (You're really close, you just need to remember the definition of the tan function a little better.)
     
  9. Apr 8, 2009 #8
    We crossed messages again ...

    Yes! tan(angle) = y/x, so now you can solve the equation you just wrote.
     
  10. Apr 8, 2009 #9
    don't worry, I've got it. Thank you!
     
  11. Apr 8, 2009 #10
    See my post.
     
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