Find the Indicated Roots $7 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

question 306

Multiple Choice

Find the indicated roots. Write the answer in polar form.
-Fifth roots of $7 \left( \cos \frac { \pi } { 3 } + i \sin \frac { \pi } { 3 } \right)$

• A) \(\sqrt [ 5 ] { 7 } \left( \cos \frac { \pi } { 15 } + \mathrm { i } \sin \frac { \pi } { 15 } \right) , \sqrt [ 5 ] { 7 } \left( \cos \frac { 7 \pi } { 15 } + \mathrm { i } \sin \frac { 7 \pi } { 15 } \right) , \sqrt [ 5 ] { 7 } \left( \cos \frac { 13 \pi } { 15 } + \mathrm { i } \sin \frac { 13 \pi } { 15 } \right)\), \(\sqrt [ 5 ] { 7 } \left( \cos \frac { 19 \pi } { 15 } + i \sin \frac { 19 \pi } { 15 } \right) , \sqrt [ 5 ] { 7 } \left( \cos \frac { 5 \pi } { 3 } + i \sin \frac { 5 \pi } { 3 } \right)\)
• B) \(\frac { 7 } { 5 } \left( \cos \frac { \pi } { 15 } + i \sin \frac { \pi } { 15 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 7 \pi } { 15 } + i \sin \frac { 7 \pi } { 15 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 13 \pi } { 15 } + i \sin \frac { 13 \pi } { 15 } \right)\), \(\frac { 7 } { 5 } \left( \cos \frac { 19 \pi } { 15 } + i \sin \frac { 19 \pi } { 15 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 5 \pi } { 3 } + i \sin \frac { 5 \pi } { 3 } \right)\)
• C) \(\frac { 7 } { 5 } \left( \cos \frac { \pi } { 15 } + i \sin \frac { \pi } { 15 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 4 \pi } { 15 } + i \sin \frac { 4 \pi } { 15 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 7 \pi } { 15 } + i \sin \frac { 7 \pi } { 15 } \right)\), \(\frac { 7 } { 5 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 13 \pi } { 15 } + i \sin \frac { 13 \pi } { 15 } \right)\)
• D) \(\sqrt [ 5 ] { 7 } \left( \cos \frac { \pi } { 15 } + i \sin \frac { \pi } { 15 } \right) , \sqrt [ 5 ] { 7 } \left( \cos \frac { 4 \pi } { 15 } + i \sin \frac { 4 \pi } { 15 } \right) , \sqrt [ 5 ] { 7 } \left( \cos \frac { 7 \pi } { 15 } + i \sin \frac { 7 \pi } { 15 } \right)\), \(\sqrt [ 5 ] { 7 } \left( \cos \frac { 2 \pi } { 3 } + i \sin \frac { 2 \pi } { 3 } \right) , \frac { 7 } { 5 } \left( \cos \frac { 13 \pi } { 15 } + i \sin \frac { 13 \pi } { 15 } \right)\)

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