For questions1 - 3,the polar coordinates of a point are given. Find the rectangular coordinates of each point. (2 points each)

1.

2.

3.

For questions4 - 6,the rectangular coordinates of a point are given. Find the polar coordinates of each point. (2 points each)

4.(4, 0)

5.(3, 4)

6.(2, -2)

7.Give two sets of polar coordinates that could be used to plot the given point. (4 points)

a.

b.

8.Identify, graph, and state the symmetries for each polar equation. Write the scale that you are using for the polar axis. (4 points)

a.r= 9cos(5)

b.r= 2cos

9.Transform each polar equation to an equation in rectangular coordinates and identify its shape. (4 points)

a.= 1.34 radians

b.r= tansec

10.Compute the modulus and argument of each complex number. (4 points)

a.-5i

b.

11.Write each complex number in rectangular form. Plot and label (witha-d) each point on the polar axes below. (4 points)

a.	b.
c.	d.

12.Letz= 13 + 7iandw= 3(cos(1.43) +isin(1.43)). (6 points)

a.Convertzto polar form.

b.Calculatezwusing De Moivre's theorem.

c.Calculateusing De Moivre's theorem.

For questions13 - 15,letand. Calculate the following, keeping your answer in polar form. (2 points each)

13.

14.

15.

For questions16 - 19,write each expression in the standard form for the complex numbera+bi.( 2 points each)

16.

17.

18.The complex fifth roots of.

19.Find all seventh roots of unity and sketch them on the axes below.