Answer:
i
Explanation:
First, let us realise that
[tex]i^4=1[/tex]
Next, we rewrite our expression as
[tex]i^{457}=i^{456}\cdot i[/tex]
Since 456 = 4 * 114, we can write the above as
[tex]i^{456}\cdot i=(i^4)^{114}\cdot i[/tex]
Since,
[tex]i^4=1[/tex]
we have
[tex]\begin{gathered} (i^4)^{114}\cdot i\Rightarrow(1)^{114}\cdot i \\ =i \end{gathered}[/tex]
Hence,
[tex]\boxed{i^{\mleft\{457\mright\}}=i\text{.}}[/tex]
which is our answer!
