Test:
Complex Numbers II - Ambitious
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Question 1:
If
(
x
+
y
)
+
(
x
−
y
)
=
5
+
3
i
, find
x
and
y
A
x
=
3,
y
=
2
B
x
=
5,
y
=
3
C
x
=
2,
y
=
0
D
x
=
4,
y
=
1
Question 2:
Express
z
=
6
+
8
i
in the polar form
A
z
=
10
(
cos
36.87
°
+
i
sin
36.87
°
)
B
z
=
14
(
cos
36.87
°
+
i
sin
36.87
°
)
C
z
=
10
(
cos
53.13
°
+
i
sin
53.13
°
)
D
z
=
10
(
sin
53.13
°
+
i
cos
53.13
°
)
Question 3:
Express
z
=
4
+
3
i
in the shortened polar form
A
z
=
7
36.87
°
B
z
=
5
53.13
°
C
z
=
4
36.87
°
D
z
=
5
36.87
°
Question 4:
Express
z
=
−
4
−
5
i
in the shortened polar form
A
z
=
9
51.34
°
B
z
=
41
51.34
°
C
z
=
41
231.34
°
D
z
=
6
231.34
°
Question 5:
Express
3
(
cos
15
°
+
i
sin
15
°
)
in the form
a
+
i
b
A
0.551
+
0.289
i
B
1.457
−
2.721
i
C
2.898
+
0.777
i
D
3
+
i
Question 6:
Express
7
(
cos
32
°
+
i
sin
32
°
)
in the form
a
+
i
b
A
5.936
+
7
i
B
3.71
+
5.936
i
C
7
+
2.56
i
D
5.936
+
3.71
i
Question 7:
Express
5
237
°
in the form
a
+
i
b
A
−
2.725
−
4.195
i
B
1.625
+
2.785
i
C
1.575
+
3.642
i
D
4.395
−
3.115
i
Question 8:
Change
3
60
°
to the exponential form
A
3
e
π
2
i
B
3
e
π
3
i
C
3
e
−
π
3
i
D
6
e
π
i
Question 9:
Change
12
210
°
to the exponential form
A
12
e
5
6
π
i
B
12
e
7
6
π
i
C
6
e
5
6
π
i
D
12
e
6
7
π
i
Question 10:
Change
7
197.5
°
to the exponential form
A
12
e
1.2
π
i
B
12
e
19
18
π
i
C
6
e
19
18
π
i
D
7
e
79
72
π
i
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