Exam Review 1!
page 1 of 4!
Trig/PreCalc!
Name________________________
06-06-16
Some Complex Number Review
Write the following in simplified a + bi form.
1.!
3(cos(45°) + isin(45°))!
!
!
3.!
!
!
!
2. [6(cos(30°) + isin(30°))]2
______________!
!
!
!
(7 + 4i)2 !
!
!
!
!
!
4.!
2i20 + 6i123
!
!
!
______________!
!
!
!
!
!
!
!
!
!
!
______________
!
!
______________
3(cos(237°) + isin(237°)) · 2(cos(60°) + isin(60°))!
!
!
!
!
______________!
(3 + 2i) – (6 – 7i)!
!
9.!
!
!
!
7.!
!
!
!
5.!
!
!
!
i2!
!
!
!
!
!
!
!
!
!
!
!
______________!
!
!
!
!
!
!
6. i52
!
!
!
!
!
!
______________
8. i0! !
!
!
!
!
______________
!
!
!
______________
!
!
!
!
______________
!
!
!
!
______________
2
3+ i
10.
!
!
!
______________!
!
!
12.! –8 – 2i
Write in polar form.
11.! 4 + 4i!
!
!
!
!
!
!
!
______________!
!
13.! 5i!
!
!
!
!
14.! –16
!
!
!
!
______________!
!
!
!
!
!
!
!
!
!
!
!
15.!What is the rectangular form of the complex number 2cis(135°)?
a) -2! !
b) ! √2 + √2i!
!
c) !
-√2 + √2i! !
d) -√2 – √2i!
Exam Review 1!
page 2 of 4!
Trig/PreCalc!
Name________________________
06-06-16
16. 2 – 2i is a fourth root of which of the following?
a) -8! !
!
!
!
b) 8i!!
!
!
c) -64!
!
!
c) 3cis(190º)!
!
!
d) 32
!
!
d) 9cis(270º)
17. Which of these is a cube root of 27cis(210º)?
a) 3cis(140º)!!
!
!
b) 9cis(70º)!
⎛ 5π ⎞
18. The rectangular coordinates of the point with polar coordinates ⎜ 6, ⎟ are
⎝ 4 ⎠
!
a) (-6√2, -6√2)!
!
b) (-3√2, -3√2)!
c) (-3√2, 3√2)!!
!
19. The polar coordinates of the point with rectangular coordinates (2√3, -2) are
⎛ 5π ⎞
⎛ 5π ⎞
!
a) ⎜ 2, ⎟ !
!
!
!
b) ⎜ 4, ⎟
⎝ 3⎠
⎝ 3⎠
!
⎛ 11π ⎞
c) ⎜ 2,
⎟!
⎝
6 ⎠
!
!
20. The complex number i 3 − i 4 +
!
!
!
⎛ 11π ⎞
d) ⎜ 4,
⎟
⎝
6 ⎠
2
is equal to
i
a) 1 + 3i! !
!
!
!
!
b) 1 – 3i
c) -1 – 3i! !
!
!
!
!
d) 3i – 1
21. The complex number (3 + 2i)(1 + 4i) is equal to
a) –5 +14i! !
!
!
!
b)!
5 + 14i
c)!
!
!
!
d)!
11 – 14i
11 + 14i!
⎛
⎛ 5π ⎞
⎛ 5π ⎞ ⎞
22. The rectangular form of the complex number z = 2 ⎜ cos ⎜ ⎟ + i sin ⎜ ⎟ ⎟ is
⎝ 6 ⎠
⎝ 6 ⎠⎠
⎝
a. -√3 + i! !
!
!
!
b. 2√3 + i!
c.!
!
!
!
d.!
-1 + √3i!
-2√3 + 2i
d) (-6√2, 6√2)
Exam Review 1!
page 3 of 4!
Trig/PreCalc!
Name________________________
06-06-16
23. The trigonometric form of the complex number –3 +3i is
a) 3cis(315°)!
c)!
!
3√2cis(315°)!
!
!
!
b)!
3cis(135°)
!
!
!
d)!
3√2cis(135°)
⎛
⎛
⎛ 3π ⎞
⎛ 3π ⎞ ⎞
⎛ 4π ⎞
⎛ 4π ⎞ ⎞
24. If z = 4 ⎜ cos ⎜ ⎟ + i sin ⎜ ⎟ ⎟ and w = 10 ⎜ cos ⎜
+ i sin ⎜
then zw equals
⎟
⎝ 5 ⎠
⎝ 5 ⎠⎠
⎝ 9 ⎠
⎝ 9 ⎟⎠ ⎟⎠
⎝
⎝
⎛
⎛ 47π ⎞
⎛ 47π ⎞ ⎞
a) zw = 14 ⎜ cos ⎜
+ i sin ⎜
! !
⎟
⎝
⎠
⎝ 45 ⎟⎠ ⎟⎠
⎝
45
⎛
⎛ 4π ⎞
⎛ 4π ⎞ ⎞
b) zw = 40 ⎜ cos ⎜
+ i sin ⎜
⎟
⎝
⎠
⎝ 15 ⎟⎠ ⎟⎠
⎝
15
⎛
⎛ 47π ⎞
⎛ 47π ⎞ ⎞
c) zw = 40 ⎜ cos ⎜
+ i sin ⎜
! !
⎟
⎝
⎠
⎝ 45 ⎟⎠ ⎟⎠
⎝
45
⎛
⎛ 4π ⎞
⎛ 4π ⎞ ⎞
d) zw = 14 ⎜ cos ⎜
+ i sin ⎜
⎟
⎝
⎠
⎝ 15 ⎟⎠ ⎟⎠
⎝
15
25. Which of the following is not a cube root of 27i?
a)
3 3 3
+ i!
2
2
c) −
!
!
!
!
3 3 3
+ i! !
2
2
!
!
!
!
b) –3i
!
d)
3 3 3
− i
2
2
26. Find (2 + 3i)4 in polar form and rectangular form.
!
!
!
!
!
!
27. Evaluate (3cis(120°)) 4 in polar and rectangular.! !
!
!
!
!
!
!
!
!
!
!
!
!
!
!
______________!
______________!
!
!
!
!
______________
!
______________
Exam Review 1!
page 4 of 4!
Trig/PreCalc!
Name________________________
06-06-16
28. Find the fourth roots of z = -81 in polar and rectangular form. Plot all roots below.
!
! ______________!
!
______________!
!
______________!!
______________
!
! ______________!
!
______________!
!
______________!!
______________
29. Find the cube roots of z = 8i in polar and rectangular form. Plot all roots below.
!
! !
!
______________!
!
______________!
!
______________
!
! !
!
______________!
!
______________!
!
______________