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Finding root of complex equation

  1. Apr 16, 2015 #1
    1. The problem statement, all variables and given/known data
    Good day,

    I've been have having difficulties finding the roots of this:
    Find the roots of 3ix^2 + 6x - i = 0
    where i = complex number
    i = sqrt(-1)

    2. Relevant equations
    quadratic formula (apologies for the large image)
    quadratic-formula.jpg

    3. The attempt at a solution

    using the quadratic formula
    [-6 (+-) sqrt (36 - 4(3i)i)] / 6i
    = (-6/6i) + (sqrt(24)/6i)
    multiplying by conjugate I get:
    =i (+-) ((-6i * sqrt(24))/ 36)

    I'm stuck here.
    apparently the roots should have both real and imaginary parts, but I have 2 imaginary parts. ie x = Re + i Im
    what exactly do I have to do next?

    Thank you.
     
  2. jcsd
  3. Apr 16, 2015 #2
    You got ##i ^+_- \frac{\sqrt(24)}{6i}##
    Now you can write it as ##i ^+_- \frac{2\sqrt(6)}{6i}##
    now 1/i=-i
    so ##i ^+_- (-i\frac{2\sqrt(6)}{6})## Now take a +/- B as a+b and a-b
     
  4. Apr 16, 2015 #3
    so, there is no real part for the left side of the answer?
    or should I express the answer as:
    (0 + i) + (−i * ((2√6)/6) ) and (0 + i) - (−i * ((2√6)/6) )
     
  5. Apr 16, 2015 #4
    oh, never mind.
    I've finally got it.


    Thank you for your time.
     
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