Computing with Complex Numbers

Simplify the following expressions:

1.

$e^{j\frac{\pi}{2}} + e^{-j\frac{\pi}{4}}$

2.

$(1+j) \cdot e^{-j\frac{\pi}{4}}$

3.

$(1+j) / e^{j\frac{\pi}{4}}$

4.

$(\frac{\sqrt{2}}{2} + j \frac{\sqrt{2}}{2})^{96}$

5.

$(\frac{\sqrt{2}}{2} + j \frac{\sqrt{2}}{2})^{100}$