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$$\phantom{=}\frac{2i}{3-4i} + 2e^{-i30^o} +3\left(\cos\frac{\pi}{4} + i\cdot\sin\frac{\pi}{4}\right)$$$$=\frac{2i(3+4i)}{(3-4i)(3+4i)} + 2\left(\underbrace{\cos30^o}_{=\sqrt3/2}-i\,\underbrace{\sin30^o}_{=1/2}\right) +3\left(\underbrace{\cos\frac{\pi}{4}}_{=1/\sqrt2} + i\cdot\underbrace{\sin\frac{\pi}{4}}_{=1/\sqrt2}\right)$$$$=\frac{6i-8}{25} + 2\left(\frac{\sqrt3}{2}-i\,\frac{1}{2}\right) +3\left(\frac{1}{\sqrt2} + i\frac{1}{\sqrt2}\right)$$$$=\frac{6i}{25}-\frac{8}{25} + \sqrt3-i +\frac{3}{\sqrt2}+i\,\frac{3}{\sqrt2}$$$$=\left(\sqrt3+\frac{3}{\sqrt2}-\frac{8}{25}\right)+i\left(\frac{6}{25}-1+ \frac{3}{\sqrt2}\right)$$$$\approx3,533371+i\,1,361320$$
