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

question 232

Multiple Choice

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

• A) \(\left\{ 2 \operatorname { cis } \frac { 3 \pi } { 8 } , 2 \operatorname { cis } \frac { 7 \pi } { 8 } , 2 \operatorname { cis } \frac { 11 \pi } { 8 } , 2 \operatorname { cis } \frac { 15 \pi } { 8 } \right\}\)
• B) \(\left\{ \operatorname { cis } \frac { 3 \pi } { 8 } , \operatorname { cis } \frac { 7 \pi } { 8 } , \operatorname { cis } \frac { 11 \pi } { 8 } , \operatorname { cis } \frac { 15 \pi } { 8 } \right\}\)
• C) \(\left\{ 16 \operatorname { cis } \frac { 3 \pi } { 8 } , 16 \operatorname { cis } \frac { 7 \pi } { 8 } , 16 \operatorname { cis } \frac { 11 \pi } { 8 } , 16 \operatorname { cis } \frac { 15 \pi } { 8 } \right\}\)
• D) \(\{ 1 , - 1 , i , - i \}\)

---

Definitions:

UCC

is the Uniform Commercial Code, a comprehensive set of laws governing commercial transactions in the United States.

Collateral

Property or assets that a borrower offers to a lender as security for a loan, which can be seized if the loan is not repaid according to the agreed terms.

Consumer Good

A tangible item produced for personal use or consumption by the general public.

UCC

The Uniform Commercial Code represents a detailed collection of statutes that oversee every commercial transaction across the United States.