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Nth Roots Complex Numbers

  1. Nov 2, 2012 #1
    1. The problem statement, all variables and given/known data

    z^2 = a + bi

    a = real number
    b = real number

    find all the solutions for z

    2. Relevant equations



    3. The attempt at a solution

    (x+y)^2 = a + bi ?
     
  2. jcsd
  3. Nov 2, 2012 #2

    Mentallic

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    Let z = x+iy

    Then

    (x+iy)^2 = a+ib.

    Expand the LHS and then compare the real parts and imaginary parts. Then what you'll have is a system of two equations in the two unknown x and y.
     
  4. Nov 2, 2012 #3
    I am stuck at:

    0= y^4 + ay^2 - b^2/4
     
  5. Nov 2, 2012 #4

    Mentallic

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    It's a quadratic in y^2. If you're unsure what that means, let some other variable such as m=y2 and then solve for m, and then convert back to y2 and solve for y.
     
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