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

question 168

Multiple Choice

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

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

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Definitions:

In Rem Jurisdiction

A legal principle that allows a court to exercise jurisdiction over a particular piece of property, regardless of who owns the property or where the owner is located.

Counterclaim

A legal claim made in response to the plaintiff’s initial claim in a civil suit. Unlike a defense, the counterclaim is the defendant’s affirmative attempt to obtain legal relief; in effect, it states a cause of action entitling the defendant to such relief. Often, the counterclaim must arise out of the occurrence that forms the basis for the plaintiff’s claim.

Compelled to Testify

The legal obligation of a witness to give testimony in a legal proceeding, even against their own interest, under penalty of law.

Affirmative Defense

A defense used in litigation where the defendant introduces evidence, which, if found to be credible, will negate criminal or civil liability, even if it is proven that the defendant committed the alleged act.