Appendix G - Complex Numbers - G Exercises - Page A56: 19

$\pm\frac{3}{2}i$

We solve for $x$: $4x^{2}+9=0$ $4x^{2}=-9$ $x^{2}=-\displaystyle \frac{9}{4} $ $x=\displaystyle \pm\sqrt{-\frac{9}{4}}$ $=\displaystyle \pm\sqrt{-1*\frac{9}{4}}$ We use the fact that $\sqrt{-1}=i$: $=\pm\sqrt{\frac{9}{4}}i$ $=\pm\frac{3}{2}i$