Final answer:
The square root and the square in the equation cancel each other out, resulting in z⁵=z⁵, which is true for all values of z. Hence, all the given options A) z=0, B) z=1, C) z=−1, D) z=2, and E) z=−2 are correct.
Step-by-step explanation:
The question asks us to solve the equation √(z⁵)²=z⁵. To solve this, we simply need to simplify the left side of the equation. The square root and the square are inverse operations, meaning they cancel each other out, leaving us with just z⁵ on both sides. Therefore, here is our step-by-step simplification:
- Start with √(z⁵)²=z⁵.
- The square root of a square cancels out, so it simplifies to z⁵=z⁵.
- Since z⁵ is equal to itself, the equation is true for all values of z.
Thus, the answer is not just a single value but any real number. Therefore, options A) z=0, B) z=1, C) z=−1, D) z=2, and E) z=−2 are all correct, as they all satisfy the equation z⁵=z⁵.