# Finding root of complex equation

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1. Apr 16, 2015

### Timmy Time

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)

3. The attempt at a solution

[-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. Apr 16, 2015

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

3. Apr 16, 2015

### Timmy Time

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) )

4. Apr 16, 2015

### Timmy Time

oh, never mind.
I've finally got it.