Question: This is what I got:

Blue: $g(x)$

Red: $f(x)$

Yellow: $(g\circ f)(x)$

Green: $(f\circ g)(x)$

[![enter image description here](https://i.stack.imgur.com/VZ87U.png)](https://i.stack.imgur.com/VZ87U.png)

Answer: 
There is a pattern:

[![enter image description here](https://i.stack.imgur.com/BWEJc.png)](https://i.stack.imgur.com/BWEJc.png)

The general graph of $(1+i)^n$ is given by, for $n\ge0$,

[![enter image description here](https://i.stack.imgur.com/bKRzu.png)](https://i.stack.imgur.com/bKRzu.png)

or,

> 
> $$(1+i)^n=2^{n/2}(\cos\frac{n\pi}4+i\sin\frac{n\pi}4)$$
> 
> 
>
Hint

Note that $(1+i)^2=2i$.

If $n=2k$ then $(1+i)^{2k}=(2i)^k$;

If $n=2k+1$ then $(1+i)^{2k+1}=(2i)^k(1+i)$.

Also remember that:

1. $i^{4p}=1$
2. $i^{4p+1}=i$
3. $i^{4p+2}=-1$
4. $i^{4p+3}=-i$

Can you finish?