PreCalculus
Chapter 8 Test
Name
Directions: Show all work and reasoning to receive full credit.


Convert the rectangular point  3 ,1 to a point in polar coordinates.
1.
10
2.
3.
 1
3 
Use DeMoivre’s Theorem to write the expression   
i  in standard form a + bi.
2
2


a. Find the 4 complex roots for
degrees.
3  1i leave your answers in polar form with the argument in
b. Sketch the roots from part a on a circle with the polar coordinates clearly identified.
4.
Given the complex numbers z  2  2i and w  3  i , determine z  w using polar notation.
5.
The vector v has initial point P(5,3) and terminal point Q(-6, -6).
Determine the unit vector having the same direction as v.
6.
Determine the angle between the vectors v = -3i -5j and w = 3i – 2j.
7.
Decompose v into two vectors v1 and v2, where v1 is parallel to w and v2 is orthogonal to w.
v = i – 2j
w = -3i + j
8.
Determine the direction angles of the vector v = 2i -3j – 4k.
9.
Determine a vector orthogonal to both v = i + 6j + k and w = -4i + 4j + 2k.
10. Determine u   v  w  given u = 3i + 3j - 4k, v = 2i + 3j - 3k, and w = 3i - 2j – 2k.
11. Show the geometric representation of the following using the given illustrations of a and b.
a
a.
a+b
b
b.
b–a
c.
4b
12.
Determine the area of the parallelogram formed by the adjacent vectors p and q in two different ways!
p = 3i – 2j + 4k
q = 4i - 3j + 5k
13. Sketch a graph of r  1 3sin  on the polar grid provided.
True or False
14.
Translating vectors changes the direction of the vector
__________
15.
The result of the cross product of two vectors is another vector
__________
16.
Parallel vectors always point in the opposite direction
__________