Question

Hi I really need help with this question, hopefully I can get some help on this thank you very much

Answer 1

It is important to note that the value of "i" is √-1.

Hence, we have:

`\begin{gathered} i^2=(\sqrt[]{-1})^2=-1_{} \\ i^3=i^2* i=-1* i=-i \\ i^4=i^2* i^2=-1*-1=1 \end{gathered}`

Using the above equivalent of i, let's split i⁷³⁵ into smaller exponents.

Let's divide 735 into 4. We get 183.75. Hence, we can have 183 i⁴ in i⁷³⁵ and that is just equal to 1.

Multiplying 183 by 4, we get 732. Hence, from 735, the only remaining "i" is 3. So, i⁷³⁵ can be split into:

`\begin{gathered} i^(735)=i^(732)* i^3 \\ i^(735)=1*-i \\ i^(735)=-i \end{gathered}`

Therefore, the value of i⁷³⁵ = -i as shown above.