Find All Solutions of the Equation $$x ^ { 5 } - 243 = 0$$

question 308

Multiple Choice

Find all solutions of the equation. Leave answers in trigonometric form.
- $$x ^ { 5 } - 243 = 0$$

• A) \(\{ 3 , - 3 \}\)
• B) \(\left\{ 3 \operatorname { cis } \frac { \pi } { 5 } , 3 \operatorname { cis } \frac { 3 \pi } { 5 } , 3 \operatorname { cis } \pi , 3 \operatorname { cis } \frac { 7 \pi } { 5 } , 3 \operatorname { cis } \frac { 9 \pi } { 5 } \right\}\)
• C) \(\left\{ 243 \operatorname { cis } 0,243 \operatorname { cis } \frac { 2 \pi } { 5 } , 243 \operatorname { cis } \frac { 4 \pi } { 5 } , 243 \operatorname { cis } \frac { 6 \pi } { 5 } , 243 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}\)
• D) \(\left\{ 3 \operatorname { cis } 0,3 \operatorname { cis } \frac { 2 \pi } { 5 } , 3 \operatorname { cis } \frac { 4 \pi } { 5 } , 3 \operatorname { cis } \frac { 6 \pi } { 5 } , 3 \operatorname { cis } \frac { 8 \pi } { 5 } \right\}\)

---

Definitions:

Reinforcements

In behavior psychology, any event that strengthens or increases the likelihood of a behavior occurring again.

Person-centered Therapist

A professional who practices a form of psychotherapy that emphasizes the importance of the individual's subjective experience and intrinsic capacity for self-healing and growth.

Transference

The redirection of feelings and desires, especially those unconsciously retained from childhood towards a new object, often observed in psychoanalytic therapy.

Electroconvulsive Therapy (ECT)

A psychiatric treatment in which seizures are electrically induced in patients to provide relief from mental disorders, primarily severe depression.