Prove that $\tan^{-1}{\frac{1}{5}} \approx \frac{\pi}{16}$ using complex number method 
Prove that $\tan^{-1}{\frac{1}{5}} \approx \frac{\pi}{16}$ using
  complex number method.
Hint: Take $z=5+i$

What is meant by complex number method in this problem? I couldn't think of do the above proof using complex numbers. Any suggestions ?

$(5+i)^4 = 476 + 480i $ Since $476$ is approximately $480$, the angle of the line from $0$ to $476 + 480i$ made with the x-axis is about $45$ degrees or $\pi/4$ radians.
So $\arctan (1/5) $ is about $\pi/4 \over 4$ or $\pi/16$.
