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!

How to get 4 roots for z^4 +16 =0?

  1. Jun 18, 2013 #1

    dla

    User Avatar

    1. The problem statement, all variables and given/known data
    Solve for z^4 +16=0


    2. Relevant equations



    3. The attempt at a solution
    What I first did was square rooted both sides to get z^2 = ±4i, but I don't how to continue from there. I'm guessing we have to find the roots from z^2=4i and then from z^2=-4i separately any help will be much appreciated!
     
  2. jcsd
  3. Jun 18, 2013 #2
    try this first;

    [tex]z^4+16=0[/tex]

    [tex](z^2+4i)(z^2-4i)=0[/tex]
     
  4. Jun 18, 2013 #3

    CAF123

    User Avatar
    Gold Member

    You could try rewriting the RHS of ##z^4 = -16## in Euler form, which may make the problem less fiddly.
     
  5. Jun 19, 2013 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    In fact, in polar form, i= e^{i\pi/2} so [itex]\sqrt{i}= e^{i\pi/4}= \sqrt{2}/2+ i\sqrt{2}/2[/itex] and [itex]e^{-i\pi/4}= \sqrt{2}/2- i\sqrt{2}{2}[/itex]

    If [itex]z^2= -4i[/itex] then [itex]z= \pm i(2)\sqrt{i}[/itex].
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted