$e$ for Euler

One may want to assume that $\frac{22}{7} = π$ , but 22/7 is only an approximation, as $\frac{22}{7} > π$ As of note, $cos(\frac{22}{7})+isin(\frac{22}{7}) \approx -0.9999992+0.0012644i$

Well, $\pi$ is never equal to $\frac{22}{7}$ . To prove this statement, You can try to solve this integral $\large \int_{0}^{1} \frac{x^4(1-x)^4}{1+x^2} \ dx$ The result would be $\frac{22}{7}-\pi$ and since area cannot be negetive, that means $\frac{22}{7}$ must be greater than $\pi$ .

Below is the graph of the function

$e^{i\cdot{n}}$ will not give you an algebraic number unless n is transcendental. $\frac {22}{7}$ isn't trancendental, so it cannot give -1 as the answer.