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!

Complex Number

  1. Dec 18, 2011 #1
    The motion of a point P in the complex plane is defined by the
    principal root of z^5= (1+ t)^i

    a)find z(t)
    b)Show that P is undergoing a circular motion. Find the velocity
    and acceleration as a function of time

    I'm pretty sure I know how to do b but I don't really understand the wording of the question. A is really confusing me. The 'Principal root' would that mean I have to take the root of both sides? and then just rearrange and isolate z?
     
  2. jcsd
  3. Dec 18, 2011 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    The function z(t) describes the motion of the point in the x,y plane. So you need to take the fifth root of both sides of the equation to get z(t). As you know, there are 5 fifth roots of a complex number, you have to take the principal one.


    ehild
     
  4. Dec 18, 2011 #3

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Ask Dr. Euler for help.

    (I have to confess, I never heard the term 'principal root' before. I believe, with deep conviction , that all roots are created equal.) :smile:
     
  5. Dec 18, 2011 #4

    Deveno

    User Avatar
    Science Advisor

    well, there is a qualitative difference between the 2 roots of z4 - 1 = 0, 1 and i, in the sense that 1 is a power of i, but not vice versa.
     
  6. Dec 18, 2011 #5

    rude man

    User Avatar
    Homework Helper
    Gold Member

    EIDT EDIT: Oops, I still get a straight line, magnitude [ln(1+t)]^0.2 and angle 0.2 rad.

    Someone else please join in?
     
    Last edited: Dec 18, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook