It is important to note that the value of "i" is √-1.
Hence, we have:
[tex]\begin{gathered} i^2=(\sqrt[]{-1})^2=-1_{} \\ i^3=i^2\times i=-1\times i=-i \\ i^4=i^2\times i^2=-1\times-1=1 \end{gathered}[/tex]
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:
[tex]\begin{gathered} i^{735}=i^{732}\times i^3 \\ i^{735}=1\times-i \\ i^{735}=-i \end{gathered}[/tex]
Therefore, the value of i⁷³⁵ = -i as shown above.
