Complex Numbers

1.

Let x=1+j. Use the diagram below to show the location of x in the complex plane.

2.

Determine the magnitude and phase of x.

3.

Let y denote the conjugate complex of x. Determine y and use the diagram below, to show the location of y in the complex plane.

4.

Determine the magnitude and phase of y.

5.

Compute x², y², and $x \cdot y$.