Find the Indicated Roots $- 1 - \sqrt { 3 } i$

question 34

Multiple Choice

Find the indicated roots. Write the answer in a + bi form.
-Fourth roots of $- 1 - \sqrt { 3 } i$

• A) \(\frac { 1 } { 4 } ( 1 + \sqrt { 3 } i ) , \frac { 1 } { 4 } ( - \sqrt { 3 } + i ) , \frac { 1 } { 4 } ( - 1 - \sqrt { 3 } i ) , \frac { 1 } { 4 } ( \sqrt { 3 } - i )\)
• B) \(\frac { \sqrt [ 4 ] { 2 } } { 2 } ( 1 + \sqrt { 3 } i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( - \sqrt { 3 } + i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( - 1 - \sqrt { 3 } i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( \sqrt { 3 } - i )\)
• C) \(\frac { 1 } { 4 } \left( 1 + \sqrt { 3 } \mathrm { i } , , \frac { 1 } { 4 } ( \sqrt { 3 } + i ) , \frac { 1 } { 4 } ( 1 - \sqrt { 3 } i ) , \frac { 1 } { 4 } ( \sqrt { 3 } - i ) \right.\)
• D) \(\frac { \sqrt [ 4 ] { 2 } } { 2 } ( 1 + \sqrt { 3 } i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( \sqrt { 3 } + i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( 1 - \sqrt { 3 } i ) , \frac { \sqrt [ 4 ] { 2 } } { 2 } ( \sqrt { 3 } - i )\)

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