Polar Coordinates And Complex Numbers Worksheets With Answers - Math 611b Page 47
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50Ex 4 p.601 AMC
Find the three cube roots of ! 2 ! 2i and check your work by graphing on the TI-83.
Solution
π
π
⎡
⎤
5
5
r =
− −
=
+
, 2 = 5 B /4
Convert ! 2 ! 2i to polar form.
2 2
2 2
i
8 cos
i
sin
⎢
⎥
⎣
⎦
4
4
F
I
F
I
1
1
θ
π
θ
π
+
+
2
2
H G
K J
H G
K J
=
+
p
p
z
r
(cos
i
sin
)
p
p
F
I
F
I
π
π
5
5
π
π
+
+
G G
J J
G G
J J
2
k
2
k
1
1
4
4
− −
=
+
3
3
(
2
2
i
)
(
2 2
) (cos
i
sin
)
G
J
G
J
3
3
H
K
H
K
π
π
1
5
5
=
− −
=
+
=
+
3
when k
0
(
2
2
i
)
2
(cos
i
sin
)
0 37
.
1 37
.
i
12
12
π
π
1
13
13
=
− −
=
+
= −
−
3
when k
1
(
2
2
i
)
2
(cos
i
sin
)
1 37
.
0 37
.
i
12
12
π
π
1
21
21
=
− −
=
+
=
−
3
when k
2
(
2
2
i
)
2
(cos
i
sin
)
1
i
12
12
Using the TI-83( and steps on p.602)
47
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