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Which of the Following Is a Fifth Root Of 2(1+i)?022 ( - 1 + i ) ? \quad 0 \quad 2

Question 92

Multiple Choice

Which of the following is a fifth root of 2(1+i) ?022 ( - 1 + i ) ? \quad 0 \quad 2
I. 810(cos(3π20) +isin(3π20) ) \sqrt [ 10 ] { 8 } \left( \cos \left( \frac { 3 \pi } { 20 } \right) + i \sin \left( \frac { 3 \pi } { 20 } \right) \right)
II. 810(cos(19π20) +isin(19π20) ) \sqrt [ 10 ] { 8 } \left( \cos \left( \frac { 19 \pi } { 20 } \right) + i \sin \left( \frac { 19 \pi } { 20 } \right) \right)
III. 25(cos(3π20) +isin(3π20) ) \sqrt [ 5 ] { 2 } \left( \cos \left( \frac { 3 \pi } { 20 } \right) + i \sin \left( \frac { 3 \pi } { 20 } \right) \right)


A) I is the only root.
B) None are roots.
C) III is the only root.
D) I and II are the only roots.
E) I and III are the only roots.

Correct Answer:

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