Evaluate $(5-i)^4 (1+i)$ then prove that $ \pi/4=4\arctan(1/5)-\arctan(1/239)$ Evaluate $(5-i)^4 (1+i)$ then prove that $ \pi/4=4\arctan(1/5)-\arctan(1/239)$


I did the first part of evaluating it manually and I got 956-4i.  However I am having trouble seeing how I can use this result to calculate $\pi/4$ in that equation.  Can anyone help me here?
I think it is about the formula 
$$e^{i\theta}=\cos\theta+i \sin\theta $$

$$(5-i)^4(1+i)=({e^{\arctan(-\frac{1}{5})i}})^4e^{\frac{\pi}{4}i}$$
$$956-4i=e^{\arctan(-\frac{4}{956}i)}=e^{-\frac{1}{239}i}$$
Since $(5-i)^4(1+i)=956-4i$,take log for both sides and you should get the answer.
I think it is about the formula 
$$e^{i\theta}=\cos\theta+i \sin\theta $$

$$(5-i)^4(1+i)=({e^{\arctan(-\frac{1}{5})i}})^4e^{\frac{\pi}{4}i}$$
$$956-4i=e^{\arctan(-\frac{4}{956}i)}=e^{-\frac{1}{239}i}$$
Since $(5-i)^4(1+i)=956-4i$,take log for both sides and you should get the answer.