Complex Numbers

1.

Simplify the following complex valued sum

$$z = \exp(j \pi/3) - \exp(-j2\pi/3).$$

2.

Show the location of all three complex numbers in a diagram of the complex plane. Be sure to label your diagram accurately.

3.

Give the answer (z) in polar form.

4.

Compute

$$z = \exp(j \pi/3) \cdot \exp(-j2\pi/3).$$