A) any integer
B) \[2\lambda \]
C) \[4\lambda +1\]
D) None of these
Correct Answer: C
Solution :
\[\frac{{{(1-i)}^{n}}}{{{(1+i)}^{n-2}}}=\frac{{{(1-i)}^{n}}}{{{(1+i)}^{n-2}}}\times \frac{{{(1-i)}^{n-2}}}{{{(1-i)}^{n-2}}}\] \[=2{{(-i)}^{n-1}}=2{{(-1)}^{\frac{n-1}{2}}}\] This is positive and real if\[\frac{n-1}{2}\]is even. Let\[\frac{n-1}{2}=2\lambda \] \[\therefore \] \[n=4\lambda +1\]
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