1. Not finding help here? Sign up for a free 30min 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!

Patterns found in complex numbers

  1. Mar 28, 2012 #1
    Patterns found in complex numbers URGENT!!!!

    • use de moivre's theorem to obtain solutions to z^n = i for n=3, 4, 5
    • generalise and prove your results for z^n = 1+bi, where |a+bi|=1
    • what happens when |a+bi|≠1?

    Relevant equations[/b]
    r = √a^2 + b^2
    z^n = r^n cis (nθ)


    This is what i have done:
    z^3=i
    z^3=i cis(0)
    z^3=cis(π/2+2kπ),k=0,1,2
    z=cis(π/6+2kπ/3),k=0,1,2
    z=cis(π/6),cis(π/6+2π/3),cis(π/6+4π/3)
    z=√3/2+0.5i,-√3/2+0.5i,- √3/2-0.5i

    but the 3rd solution is incorrect, should be -i. what have i done wrong?
     
  2. jcsd
  3. Mar 29, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    welcome to pf!

    hi lll030lll! welcome to pf! :smile:
    dunno, but π/6+4π/3 = 9π/6 :redface:

    (personally, i find degrees easier … 30°, 30° ± 120° :wink:)
     
  4. Mar 29, 2012 #3
    Re: Patterns found in complex numbers URGENT!!!!

    anyway, got it right in using a+bi=re^iθ
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Patterns found in complex numbers
  1. Complex Numbers (Replies: 2)

  2. Complex numbers (Replies: 6)

  3. Complex numbers (Replies: 6)

Loading...