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

  1. Jun 18, 2013 #1


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    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;


  4. Jun 18, 2013 #3


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    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


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    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].
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