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Question Number 185821 by Rupesh123 last updated on 28/Jan/23

Answered by qaz last updated on 28/Jan/23

$$5\arctan \frac{1}{7}+2\arctan \frac{3}{79}=5Arg(7+i)+2Arg(79+3i)$$$$=Arg[{(7+i)}^5\cdot {(79+3i)}^2]=Arg\left[78125000(1+i)\right]$$$$=\arctan \frac{78125000}{78125000}=\frac{\pi }{4}$$

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