Find All Solutions of the Equation $$x ^ { 2 } + 1 - \sqrt { 3 } i = 0$$

Multiple Choice

Find all solutions of the equation. Leave answers in trigonometric form.
- $$x ^ { 2 } + 1 - \sqrt { 3 } i = 0$$

A) $\left\{ \sqrt { 2 } \operatorname { cis } 60 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 240 ^ { \circ } \right\}$
B) $\left\{ 2 \operatorname { cis } 90 ^ { \circ } , 2 \operatorname { cis } 270 ^ { \circ } \right\}$
C) $\left\{ 2 \sqrt { 2 } \operatorname { cis } 90 ^ { \circ } , - 2 \sqrt { 2 } \operatorname { cis } 270 ^ { \circ } \right\}$
D) $\left\{ 2 \operatorname { cis } 45 ^ { \circ } , 2 \operatorname { cis } 225 ^ { \circ } \right\}$