Question

Hi I need help with this question please and thank u!

Answer 1

i

Step-by-step explanation:

First, let us realise that

`i^4=1`

Next, we rewrite our expression as

`i^(457)=i^(456)\cdot i`

Since 456 = 4 * 114, we can write the above as

`i^(456)\cdot i=(i^4)^(114)\cdot i`

Since,

`i^4=1`

we have

`\begin{gathered} (i^4)^(114)\cdot i\Rightarrow(1)^(114)\cdot i \\ =i \end{gathered}`

Hence,

`\boxed{i^{\mleft\{457\mright\}}=i\text{.}}`

which is our answer!