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

question 21

Multiple Choice

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

• 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.

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