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!

Cartesian to polar confusion (simple)?

  1. Mar 18, 2014 #1
    1. The problem statement, all variables and given/known data
    Convert -2+2√3i to polar coordinates.

    2. Relevant equations
    r = √x2+y2
    θ = tan-1(y/x)

    3. The attempt at a solution
    I am confused because θ = tan-1(2√3/2) = tan-1(√3) = -π/3 and r = 4, so that would make the polar form 4cis(-π/3), but the calculator gives: 4cis(2π/3).
    I think the calculator is right because when I convert my answer (4cis(-π/3)) back to cartesian it gives -2-2√3i, whereas the other (4cis(2π/3))gives the right answer, -2+2√3i.

    Can someone explain what I'm doing wrong?
    Thanks. :)
     
  2. jcsd
  3. Mar 18, 2014 #2

    arildno

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    In which quadrant does your complex number lie?
    For which interval of angles is the standard tangent function defined?
     
  4. Mar 18, 2014 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Tangent is, of course, periodic and your calculator can give only one value- the "principal" value which, for tangent, is the value of [itex]\theta[/itex] with the smallest absolute value. Since tangent is periodic with period [itex]\pi[/itex], [itex]tan(-\pi/3)= tan(-\pi/3+ \pi)= tan(2\pi/3)[/itex].

    You distinguish between them by noting that [itex]-\pi/3[/itex] is in the fourth quadrant, (+,-), while [itex]2\pi/3[/itex] is in the second quadrant, (-, +).
     
  5. Mar 18, 2014 #4
    OK, I have found the angle using x and y (cos and sin) and they both confirm that the calculator is correct. And yes, it does make sense since the complex number lies in quadrant 1 but why is the tan function wrong? I'm guessing you were hinting at that part but I really don't know. :)
     
  6. Mar 18, 2014 #5

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Are you sure that -2+2SQRT(3)i is in the first quadrant? Why don't you make a sketch?
     
  7. Mar 18, 2014 #6
    Yes that makes sense. Thanks.
    P.S I know the quadrants haha I misstyped :)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Cartesian to polar confusion (simple)?
  1. Polar to Cartesian (Replies: 1)

  2. Cartesian to polar (Replies: 4)

  3. Cartesian to polar (Replies: 2)

Loading...