Download For the given initial and terminal points, find the vector u in the form

Precalculus C
Sections 6/3 – 6/5
Review Worksheet
For the given initial and
terminal points, find the
vector u in the form
requested.
1. I: (2,7) T: (9,4)
2. I: (-1,0) T: (3,-2)
Find the magnitude and
angle direction of the
vector.
3. u = < -4, 3 >
4. u = < 0, 3 >
u = 2i + 3j and v = -4i + j
Find :
5. u + v
6. u – v
7. 2u – 5v
Find a unit vector in the
same direction as the given
vector.
8. v = < -8, -6 >
9. v = < 1, 2 >
Find the dot product of the
vectors.
10. < 3, 7 > < -1, 0 >
11. < 4, -1 > < 2, 3 >
Find the angle between the
two vectors.
12. < -1, 3 > and < 2, 5 >
13. < 3, 2 > and < -4, 0 >
Find the dot product of the
vectors.
14. ║u║ = 8 ║v║ = 10
 between u and v : 60
15. ║u║ = 20 ║v║ = 50
 between u and v : 135
z2 = 2∙cis 90
29. z1 = 30∙cis 110
z2 = 40∙cis 115
Are u and v orthogonal,
parallel, or neither?
Find the quotient of the two
complex numbers. Give the
result in standard form.
16. u =
v=
17. u =
v=
18. u =
v=
< 4, 2 >
< -3, 6 >
< 5, -2 >
< -10, 4 >
< 4, 7 >
< -11, -6 >
Find the absolute value of
the complex number.
19. -8 + 15i
20. 3i
21. 7 - i
Convert the complex
number to trigonometric
form.
22.
23.
24.
24.
2 - 2i
-6 + 8i
-7i
6
Convert the complex
number to standard form.
25. 6 2 ∙cis315
26. 5∙cis270
26. 7∙cis0
Find the product of the two
complex numbers. Give the
result in standard form.
27. z1 = 4∙cis 100
z2 = 5∙cis 50
28. z1 = 3∙cis 180
30. z1 = 12∙cis 70
z2 = 3∙cis 40
31. z1 = 3∙cis 150
z2 = 6∙cis 60
32. z1 = 24∙cis 40
z2 = 12∙cis 100
Find the power of the
complex number. Give the
result in standard form.
33. z = 2∙cis 30. Find z3.
34. z = -1∙cis 5. Find z9.
36. z = 5∙cis 135. Find z2.
Find a root of the complex
number. Give the result in
standard form.
37. A square root of
16∙cis 240.
38. A cube root of
1000∙cis 270.
39. A fifth root of
-32∙cis 150.
Find the power of the
complex number. Give the
result in standard form.
40. z = 1 + i. Find z8
41. z = 8 - 6i. Find z3