Answer
Please see below.
Work Step by Step
By using the identity $e^{i \theta }= \cos \theta + i \sin \theta$, we have$$e^{\frac{\pi i}{4}}=\cos \frac{\pi }{4} + i \sin \frac{\pi }{4}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i.$$Now, we plot the complex number $z=\frac{\sqrt{2}}{2}+ \frac{\sqrt{2}}{2}i$ the same way we plot $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ in the rectangular coordinate system.
