Consider the complex number z given below in rectangular form, and marked on the complex coordinate plane. Follow the instructions below to determine all FOURTH roots of z and mark the graph as indicated: 9 9√3 2 (1) Rewrite z in polar form (radians): Z= 9 cos = W₁ = (2) Use de Moivre's Root Theorem to determine the FOURTH roots of z in polar form, in order of increasing angles [0, 2π): W₂= W3 = Wo= W₁ = 4T W₂ = +isin (3) Convert all roots to rectangular form: W3 = ())- 3 -4 Clear All Draw: / Int
Consider the complex number z given below in rectangular form, and marked on the complex coordinate plane. Follow the instructions below to determine all FOURTH roots of z and mark the graph as indicated: 9 9√3 2 (1) Rewrite z in polar form (radians): Z= 9 cos = W₁ = (2) Use de Moivre's Root Theorem to determine the FOURTH roots of z in polar form, in order of increasing angles [0, 2π): W₂= W3 = Wo= W₁ = 4T W₂ = +isin (3) Convert all roots to rectangular form: W3 = ())- 3 -4 Clear All Draw: / Int
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Consider the complex number z given below in rectangular form, and marked on the complex coordinate
plane. Follow the instructions below to determine all FOURTH roots of z and mark the graph as indicated:
9 9√3
2
(1) Rewrite z in polar form (radians):
Z= 9 cos
wo ==
W₁ =
(2) Use de Moivre's Root Theorem to
determine the FOURTH roots of z in polar
form, in order of increasing angles [0, 2π):
W₂=
W3 ==
Wo=
W₁ =
4T
W₂ =
+isin
(3) Convert all roots to rectangular form:
W3 =
(4)) -
3
(4) Mark all roots on the coordinate plane
(5) Draw a line from the origin to each
root
4
Clear All Draw: /
Int](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3578f266-3157-43d3-ab12-11703d872a13%2F4ba44372-79eb-4776-b570-f6b9aa2a5045%2Fnscuog3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the complex number z given below in rectangular form, and marked on the complex coordinate
plane. Follow the instructions below to determine all FOURTH roots of z and mark the graph as indicated:
9 9√3
2
(1) Rewrite z in polar form (radians):
Z= 9 cos
wo ==
W₁ =
(2) Use de Moivre's Root Theorem to
determine the FOURTH roots of z in polar
form, in order of increasing angles [0, 2π):
W₂=
W3 ==
Wo=
W₁ =
4T
W₂ =
+isin
(3) Convert all roots to rectangular form:
W3 =
(4)) -
3
(4) Mark all roots on the coordinate plane
(5) Draw a line from the origin to each
root
4
Clear All Draw: /
Int
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