Answer
$x = 1.817-0.550~i$
$x = -1.817+0.550~i$
Work Step by Step
$x^2-3+2i = 0$
$x^2 = 3-2i$
We can find $r$:
$r = \sqrt{(3)^2+(-2)^2} = \sqrt{13}$
Note that $~~3-2i~~$ is in the fourth quadrant:
$tan~\theta = -\frac{2}{3}$
$\theta = tan^{-1}(-\frac{2}{3})$
$\theta = -33.69^{\circ}$
We can find $x$:
When $k=0$:
$x = (\sqrt{13})^{1/2}(cos~\frac{-33.69^{\circ}+360^{\circ}~k}{2}+i~sin~\frac{-33.69^{\circ}+360^{\circ}~k}{2})$
$x = (\sqrt{13})^{1/2}~[cos~(-16.85^{\circ})+i~sin~(-16.85^{\circ})]$
$x = 1.817-0.550~i$
When $k=1$:
$x = (\sqrt{13})^{1/2}(cos~\frac{-33.69^{\circ}+360^{\circ}~k}{2}+i~sin~\frac{-33.69^{\circ}+360^{\circ}~k}{2})$
$x = (\sqrt{13})^{1/2}(cos~163.15^{\circ}+i~sin~163.15^{\circ})$
$x = -1.817+0.550~i$
