Find All Solutions of the Equation $$x ^ { 4 } + 16 = 0$$

question 288

Multiple Choice

Find all solutions of the equation. Leave answers in trigonometric form.
- $$x ^ { 4 } + 16 = 0$$

• A) \(\left\{ \sqrt { 2 } \operatorname { cis } 45 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 315 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 135 ^ { \circ } , \sqrt { 2 } \operatorname { cis } 225 ^ { \circ } \right\}\)
• B) \(\left\{ \sqrt { 3 } \operatorname { cis } 26.565 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 333.435 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 153.435 ^ { \circ } , \sqrt { 3 } \operatorname { cis } 206.565 ^ { \circ } \right\}\)
• C) \(\left\{ 16 \right.\) cis \(45 ^ { \circ } , 16\) cis \(315 ^ { \circ } , 16\) cis \(135 ^ { \circ } , 16\) cis \(\left. 225 ^ { \circ } \right\}\)
• D) \(\left\{ 2 \operatorname { cis } 45 ^ { \circ } , 2 \operatorname { cis } 315 ^ { \circ } , 2 \operatorname { cis } 135 ^ { \circ } , 2 \operatorname { cis } 225 ^ { \circ } \right\}\)

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Definitions:

Major Premise

The first principle or statement in a deductive argument from which a conclusion is derived.

Valid Syllogism

A form of deductive reasoning where, from two given premises, a logically inevitable conclusion is derived.

I Proposition

In the traditional square of opposition, an I proposition is a form of categorical proposition which affirms some, but not necessarily all, members of a class are included in another class.

Validity Rules

Principles or guidelines used to determine the logical correctness of an argument, ensuring that if the premises are true, the conclusion must also be true.