Exponential conversion

Question

While solving Fourier series coefficients if found this problem. Anyone help me to tell that how they converted $\frac{1}{2}e^{j\pi/4}=\frac{\sqrt{2}}{4}(1+j)$

Answer 1

Hint (assuming you have $j^2=-1$): Use $e^{jx}= \cos x + j \sin x$ and $\cos \frac{\pi}{4}=\sin \frac{\pi}{4}=\frac{\sqrt{2}}{2}$

Edit- Here the completed answer after reading your comment: $$\frac{1}{2}e^{j\pi/4}=\frac{1}{2}\left(\cos \frac{\pi}{4} + j \sin \frac{\pi}{4} \right)= \frac{1}{2}\left(\frac{\sqrt{2}}{2} + j\frac{\sqrt{2}}{2}\right)=\frac{\sqrt{2}}{4}\Big(1+j\Big)$$