Polar Coordinates And Complex Numbers Worksheets With Answers - Math 611b Page 49
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50Ex 5 p.603 AMC
! 32 = 0.
5
Solve for all roots x
Solution:
5
x
= 32 This reads as: find the fifth roots of 32.
32 = 32 + 0i = 32(cos 0 + isin 0)
r = 32, 2 = 0, p = 5, k = 0,1,2,3,4
θ
π
θ
π
+
+
1
1
⎛
⎞
⎛
⎞
2
k
2
k
=
+
n
n
⎜
⎟
⎜
⎟
z
r
(cos
i
sin
)
⎝
⎠
⎝
⎠
n
n
1
1
=
+
=
=
5
n
32
32 (cos 0
i
sin 0)
2
k
0
π
π
1
1
2
2
=
+
=
+
=
5
5
32
32 (cos
i
sin
) .62 1.90
i k
1
5
5
π
π
1
1
4
4
=
+
= −
+
=
32
5
32 (cos
5
i
sin
)
1.62 1.18
i k
2
5
5
π
π
1
1
6
6
=
+
= −
−
=
5
5
32
32 (cos
i
sin
)
1.62 1.18
i k
3
5
5
π
π
1
1
8
8
=
+
=
−
=
5
5
32
32 (cos
i
sin
) .62 1.90
i k
4
5
5
ss Trace and <
Pre
cursor through the roots
The points are vertices of a regular pentagon and are concyclic in nature. That is they are equally spaced
on a circle.
49
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