How to find the imaginary roots of polynomials I'm looking for a simple way to calculate roots in the complex numbers.
I'm having the polynomial $2x^2-x+2$
I know that the result is $1/4-$($\sqrt{15}/4)i$.
However I'm not aware of an easy way to get there.

$$2x^2 - x +2 = 2\left(x^2 - \dfrac{x}2 + 1 \right) = 2\left(\underbrace{x^2 - 2 \times x \times \dfrac14 + \left(\dfrac14 \right)^2}_{a^2 - 2ab + b^2 = (a-b)^2} - \left(\dfrac14 \right)^2 + 1  \right) = 2 \left( \left(x- \dfrac14 \right)^2 + \dfrac{15}{16}\right)$$
Setting the above to zero, we get that
$$\left(x- \dfrac14 \right)^2 + \dfrac{15}{16} = 0 \implies \left(x- \dfrac14 \right)^2 = \dfrac{-15}{16} \implies x - \dfrac14 = \pm\dfrac{i\sqrt{15}}{4}$$
Hence, $$x = \dfrac{1 \pm i \sqrt{15}}4$$
