Given that

$$\iota =\sqrt{-1}$$

$$\frac{\iota +{\iota }^4+{\iota }^3}{{\iota }^3+{\iota }^4+{\iota }^5}=?$$

As we know that

$${\iota }^2=-1,{\iota }^4=1,{\iota }^3=-\iota$$

So,

$$\therefore \frac{\iota +{\iota }^4+{\iota }^3}{{\iota }^3+{\iota }^4+{\iota }^5}=\frac{\iota -1-\iota }{-\iota +1+\iota }=-\frac{1}{1}$$

$$=-1$$