Find All Solutions of the Equation $$x ^ { 2 } - i = 0$$

question 209

Multiple Choice

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

• A) \(\left\{ \operatorname { cis } 180 ^ { \circ } , \operatorname { cis } 0 ^ { \circ } \right\}\)
• B) \(\left\{ \operatorname { cis } 315 ^ { \circ } , \operatorname { cis } 135 ^ { \circ } \right\}\)
• C) \(\left\{ \operatorname { cis } 270 ^ { \circ } , \operatorname { cis } 90 ^ { \circ } \right\}\)
• D) \(\left\{ \operatorname { cis } 45 ^ { \circ } \right.\), cis \(\left. 225 ^ { \circ } \right\}\)

---

Definitions:

Valence Bond Theory

A theory that explains how electrons are shared between atoms to form chemical bonds, focusing on the concept of hybridization of atomic orbitals.

Orbitals

Mathematical functions describing the regions around an atom where electrons are most likely to be found.

Electrons

Subatomic particles with a negative electric charge, found in all atoms, responsible for chemical bonding and carrying electric current in conductors.

P Orbitals

P orbitals refer to the dumbbell-shaped orbitals in an atom, oriented orthogonally across three dimensions, and are capable of holding up to six electrons in three pairs.