Question

solve it guys..... ​

Answer 1

$\tt (\frac{1 + i}{1 - i})^{4n+1} \\ \tt = (\frac{1 + i}{1 - i} \times \frac{1 + i}{1 + i})^{4n+1} \\ \tt = (\frac {(1 + i)²}{1 - i²})^{4n+1} \\ \tt = (\frac{1 - 1 + 2i}{1 - (-1)})^{4n+1} \\ \tt = (\frac {2i}{2})^{4n+1} \\ \tt = i^{4n+1} \\ \tt = i^{4n} \times i \\ \tt = 1 \times i \\ \tt = i$