Question Number 216746 by sniper237 last updated on 17/Feb/25
$${Calculate}\:\frac{\left(\mathrm{5}+{i}\right)^{\mathrm{4}} }{\mathrm{239}+{i}}\:{Then}\: \\ $$$${Prove}\:{the}\:{Machin}\:{formula} \\ $$$$\mathrm{4}{arctan}\left(\frac{\mathrm{1}}{\mathrm{5}}\right)−{arctan}\left(\frac{\mathrm{1}}{\mathrm{239}}\right)=\frac{\pi}{\mathrm{4}} \\ $$