Question

$$-\sqrt{2}\sin(\frac{6}{x})=3$$

Solve for x (complex solution)

$x=6i\left(\ln(\left(-\frac{3}{2}i\right)\times 2^{\frac{1}{2}}+\frac{1}{2}i\times 14^{\frac{1}{2}})+2i\pi n_{1}\right)^{-1}\text{, }n_{1}\in \mathrm{Z}\text{, }not(n_{1}=\frac{1}{2}i\ln(\left(-\frac{3}{2}i\right)\times 2^{\frac{1}{2}}+\frac{1}{2}i\times 14^{\frac{1}{2}})\pi ^{-1})$
$x=6i\left(\ln(\left(-\frac{3}{2}i\right)\times 2^{\frac{1}{2}}+\left(-\frac{1}{2}i\right)\times 14^{\frac{1}{2}})+2i\pi n_{2}\right)^{-1}\text{, }n_{2}\in \mathrm{Z}\text{, }not(n_{2}=\frac{1}{2}i\ln(\left(-\frac{3}{2}i\right)\times 2^{\frac{1}{2}}+\left(-\frac{1}{2}i\right)\times 14^{\frac{1}{2}})\pi ^{-1})$