Find the following powers of the imaginary unit:

- $$i^{117}$$
- $$i^{43}$$

See development and solution

### Development:

- In this case, $$117$$ is divided by $$4$$ and we obtain a reminder of $$1$$. So, $$i^{117}=i^1=i$$.
- In this case, $$43$$ is divided by $$4$$ and we obtain a reminder of $$3$$. So, $$i^{43}=i^3=-1$$.

### Solution:

- $$i$$
- $$-i$$