e^{i 3 \frac{\pi }{4}}=e^{i \left(4\frac{\pi }{4}-\frac{\pi }{4}\right)}=e^{i \pi }e^{-i \frac{\pi }{4}}=-\left(\cos \left(\frac{\pi }{4}\right)-i \sin \left(\frac{\pi }{4}\right)\right)