An answer to a comlex equation I was working on was $$z = \frac{1}{2} + \frac{i}{2}$$ My teacher further developed it to be $$e^{\frac{i\pi}{4}-\frac{1}{2}\ln{2}}$$ And here's what I tried: $$z = \frac{1}{2} + \frac{i}{2} = z = \frac{1}{\sqrt{2}}e^{\frac{i\pi}{4}} = e^{\frac{1}{2}\ln{2}}e^{\frac{i\pi}{4}} = e^{\frac{1}{2}\ln{2}+\frac{i\pi}{4}}$$
I feel this is stupid, but I can't see why we have different answers. Anyone? Thanks!