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!

Getting the argand with De Moires theorem

  1. Mar 16, 2010 #1
    Hi just did an interesting question which made me wonder about solving it another way around

    z = 2 + 5i
    find the value of [/tex]z^{\frac{1}{4}}[/tex] which lies in the second quadrant of the Argand diagram and enter it's argument

    So [tex]arctan(5/2) \approx 1.1902 [/tex]

    We use De Moivre's Thereom and the the oscillation of the trigonometric functions
    [tex]\sqrt{29}(cos(\frac{1.1902 + 2k\pi}{4}) + isin(\frac{1.1902 + 2k\pi}{4}))

    So to lie in the second quadrant the angle must be [tex]\theta > \frac{\pi}{2}[/tex]
    [tex]\theta > \frac{ \pi}{2}[/tex]
    [tex]\frac{1.1902 + 2k\pi}{4} > \frac{\pi}{2}[/tex]

    so k > 0.8 so k > 0 (where k is an integer)

    The next integer after 0 is 1! So sub k = 1 into [tex]\frac{1.1902 + 2\pi}{4}[/tex]

    then convert to degrees 107° agreed???

    BUT how come if we say:
    To lie in the second quadrant [tex]\theta < \pi[/tex]

    [tex]\frac{1.1902 + 2k\pi}{4} < \pi[/tex]
    solves k < 2.8 so if where an integer k can take the ranges 1 to 2.

    BUT if we put 2 in:
    [tex]\frac{1.1902 + 4\pi}{4}[/tex] this is greater than [tex]\pi[/tex]

  2. jcsd
  3. Mar 16, 2010 #2


    User Avatar
    Homework Helper
    Gold Member

    No it doesn't, try solving this inequality again, and show your steps if you get the same result.
  4. Mar 16, 2010 #3
    im an idiot :blushing:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Getting argand Moires Date
Probability of getting 3 out of 4 numbers correct Sunday at 2:40 AM