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

question 113

Multiple Choice

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

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

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Definitions:

Surface Tension

The elastic tendency of a fluid surface which makes it acquire the least surface area possible, due to intermolecular forces.

Adhesive Forces

Attractive forces between unlike substances, such as water molecules adhering to glass surfaces.

Cohesive Forces

The attractive forces between like molecules that are responsible for the tendency of certain materials to stick together.

DNA Replication

The process by which DNA is duplicated; ordinarily a semiconservative process in which a double helix gives rise to two double helices, each with an "old" strand and a newly synthesized strand.