As the value of the integer exponent n increases, the trajectory of the tip of vector [math]p_n=\left(1+\frac{i\alpha}{n}\right)^n[/math] tends to settle on the unit circle in the Argand-Gauss plane, while the vector [math]p_{_{_n}}[/math] tends to overlap with the vector [math]u_{\alpha}[/math]. This confirms Euler's formula [math]e^{i\alpha}=cos\alpha+isin\alpha[/math]