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: Engineering Math - Complex Roots and Powers

  1. Sep 30, 2011 #1
    1. The problem statement, all variables and given/known data
    Evaluate the following in x+iy form.

    2. Relevant equations

    3. The attempt at a solution
    i3+i = i3*ii

    I understand how it all works out except [itex]\frac{pi}{2}[/itex]. I can't figure out how they got [itex]\frac{pi}{2}[/itex] in the first place. Any ideas? Thanks in advance.
  2. jcsd
  3. Sep 30, 2011 #2


    User Avatar

    Staff: Mentor

    My editor won't allow greek letters, so in place of theta I'll use T

    You know: eiT=cosT + i.sinT

    So let T=Pi/2, so that cosT=0, and we have

    ei.Pi/2= i

    Q: How do you say in words: rei.theta

    I'm wondering what the r is part of?
  4. Sep 30, 2011 #3


    User Avatar
    Science Advisor

    If [itex]y= i^i[/itex], then [itex]ln(y)= i ln(i)[/itex]. Further, i has modulus r= 1 and argument [itex]\theta= \pi/2[/itex] so that [itex]i= e^{i(\pi/2+ 2k\pi)}[/itex] for k any integer ([itex]e^{2k\pi}= 1[/itex] for all integer k so these are all different ways of writing i). Then [itex]ln(i)= i(\pi/2+ 2k\pi)[/itex] and so [itex]ln(y)= -(\pi/2+ 2k\pi)[/itex].
  5. Sep 30, 2011 #4
    The r comes from converting x+iy (rectangular coordinates) to polar coordinates.
    As far as how r is used, I'm unsure. None of the problems I have been given/done have used that r at all.
  6. Sep 30, 2011 #5
    Thank you both for the explanations! You're my heroes.
  7. Sep 30, 2011 #6


    User Avatar

    Staff: Mentor

    I guessed that r was the magnitude, but you confused me by introducing it in (3) for i= and I know i has a magnitude of unity. The square root of (cos2 + sin2) is always 1.

    I just wanted to make sure "re" wasn't a combination that I am unfamiliar with.

    Well, 5.cosT + 5.i.sinT would equal 5.eiT so that's when it's needed.
  8. Sep 30, 2011 #7
    Yeah, I think you're probably right. Thanks again! :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook