Suppose $\theta \neq \frac pq * \pi$. Show ${\{e^{in\theta} : n \ \epsilon \ N}\}$ is dense in $S^1=\{x + iy: x^2 + y^2 = 1\} \subseteq C$

Question

Essentially, I need to show that e^inx is dense in the complex unit circle for irrational angle x. I'm not sure how to go about this but I think I need to show that between any two points on the unit circle, we can find some e^inx.

Answer 1

Its so simple.$$exp(jx)=cos(x)+jsin(x)$$. Since $$sin^2(x)+cos^2(x)=1$$ this complex number always is on the circumference of a circle with radius 1