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How do i solve this kind of equations?

  1. May 17, 2017 #1
    1. The problem statement, all variables and given/known data
    What is the value of x and y , when (x+iy) ^2=5+4i?

    2. Relevant equations


    3. The attempt at a solution
    (x+iy)^2=5+4i

    x^2+2xiy-y^2=5+4i
     
    Last edited by a moderator: May 17, 2017
  2. jcsd
  3. May 17, 2017 #2

    berkeman

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    Staff: Mentor

    Good. Now keep going -- equate the real and imaginary parts and solve the 2 simultaneous equations...
     
  4. May 17, 2017 #3
    Equate the imagnary and real part. Like if ##x +iy = 3+i5## then I equate to get ##x = 3## and ##y = 5##.
    Though there are other ways to take square root of complex numbers.

    EDIT :
    I did not see post by @berkeman. Sorry don't mean to copy it.
     
  5. May 17, 2017 #4
    The two equations are difficult to solve simultaneously. You can solve graphically for the intercept. Both equations are hyperbolas (one is rotated). Alternatively to solve without graphics you should express 5 + 4i in polar form and then take the square root.
     
  6. May 17, 2017 #5

    Ray Vickson

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    Science Advisor
    Homework Helper

    They are not very difficult to solve simultaneously. Using the equation for the imaginary part gives a formula for y in terms of x. Then substituting that formula into the equation for the real part gives a quadratic equation in x2, which is easily solved using standard formulas.
     
  7. May 17, 2017 #6
    Yes, That is interesting. Expressing in polar form and taking square root is OK too.
     
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