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. Then, check the correct answers in the table below. If none of these answers appears correct, write your answer in the last row.

Note: Check one answer in each column.

Magnitude	Phase
$\bigcirc$ 1	$\bigcirc$ 0
$\bigcirc$ $\sqrt{2}$	$\bigcirc$ $\frac{3\pi}{4}$
$\bigcirc$ $\frac{\sqrt{2}}{2}$	$\bigcirc$ $\frac{\pi}{4}$
$\bigcirc$ 2	$\bigcirc$ $-\frac{3\pi}{4}$
$\bigcirc$ Other:	$\bigcirc$ Other:

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.Then, check the correct answers in the table below. If none of these answers appears correct, write your answer in the last row.

Note: Check one answer in each column.

Magnitude	Phase
$\bigcirc$ 1	$\bigcirc$ 0
$\bigcirc$ $\sqrt{2}$	$\bigcirc$ $\frac{3\pi}{4}$
$\bigcirc$ $\frac{\sqrt{2}}{2}$	$\bigcirc$ $\frac{\pi}{4}$
$\bigcirc$ 2	$\bigcirc$ $-\frac{3\pi}{4}$
$\bigcirc$ Other:	$\bigcirc$ Other:

5.

Compute x², y², and $x \cdot y$.Then, check the correct answers in the table below. If none of these answers appears correct, write your answer in the last row.

Note: Check one answer in each column.

x2	y2	$x \cdot y$
$\bigcirc$ j	$\bigcirc$ j	$\bigcirc$ j
$\bigcirc$ 2j	$\bigcirc$ 2j	$\bigcirc$ 2j
$\bigcirc$ -j	$\bigcirc$ -j	$\bigcirc$ -j
$\bigcirc$ -2j	$\bigcirc$ -2j	$\bigcirc$ -2j
$\bigcirc$ -2	$\bigcirc$ -2	$\bigcirc$ -2
$\bigcirc$ 2	$\bigcirc$ 2	$\bigcirc$ 2
$\bigcirc$ Other:	$\bigcirc$ Other:	$\bigcirc$ Other: