To evaluate the expression [tex]\(i^0 \times i^1 \times i^2 \times i^3 \times i^4\)[/tex], let's break it down step by step:
1. Calculate each power of [tex]\(i\)[/tex]:
- [tex]\(i^0 = 1\)[/tex]
- [tex]\(i^1 = i\)[/tex]
- [tex]\(i^2 = -1\)[/tex]
- [tex]\(i^3 = -i\)[/tex]
- [tex]\(i^4 = 1\)[/tex]
2. Multiply all the calculated powers:
- [tex]\(i^0 \times i^1 \times i^2 \times i^3 \times i^4\)[/tex]
- [tex]\(= 1 \times i \times (-1) \times (-i) \times 1\)[/tex]
3. Simplify step by step:
- First multiply [tex]\(1\)[/tex] by [tex]\(i\)[/tex]:
[tex]\[1 \times i = i\][/tex]
- Next, multiply the result by [tex]\(-1\)[/tex]:
[tex]\[i \times (-1) = -i\][/tex]
- Then, multiply by [tex]\(-i\)[/tex]:
[tex]\[-i \times (-i) = (-i) \times (-i) = i^2 = -1\][/tex] (since [tex]\(i^2 = -1\)[/tex])
- Finally, multiply by [tex]\(1\)[/tex]:
[tex]\[-1 \times 1 = -1\][/tex]
So, the value of the expression [tex]\(i^0 \times i^1 \times i^2 \times i^3 \times i^4\)[/tex] is [tex]\(-1\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{-1} \][/tex]
