Math 142
Summer 1999
Exam 4
1.
(12 pt) Write the
following complex numbers in polar (distance and angle) form
a) 
b) 
2.
(6pt) I have a complex
number that is 6 units from the origin and has angle 
. Write this complex number in the form 
.
3.
(18pt) a) Find the 6th
roots of –64.
(6 pt) b) Find the square roots of 
.
4.
(45 pt) Consider the
points 
and 
. Find the following:
a) 
and 
b)
.
c)
d)
The scalar projection
of 
on 
.
e)
The vector projection
of 
on 
.
f)
The angle between 
and 
.
g)
Find a unit vector in
the direction of the vector 
h)
Find the vector 
i)
Draw and label the
vectors 
, 
, 
, and 
5.
(15 pt) A plane is
attempting to fly in the direction 200° with airspeed of 500 miles per hour. Its actual ground
speed is 210° at 450 miles per hour.
What is the direction and speed of the wind?
6.
(8 pt) A constant
force 
is applied to a
particle as it moves from the point (-3,2) to the point (2,6). Find the work
done. (You can assume distances are in feet and force is in pounds).