AP EAMCET · Maths · Complex Number
If \(\mathrm{m}, \mathrm{n}\) are respectively the least positive and greatest negative integer values of \(k\) such that \(\left(\frac{1-i}{1+i}\right)^k=-i\), then \(m-n=\)
- A 4
- B 0
- C 6
- D 2
Answer & Solution
Correct Answer
(A) 4
Step-by-step Solution
Detailed explanation
\(\text { Given }\left(\frac{1-i}{1+i}\right)^k=-i \Rightarrow\left\{\frac{(1-i)^2}{2}\right\}^k=-i \Rightarrow(-i)^k=-i\) If \(k=1\) (least positive integer) \(\Rightarrow(-i)^1=-i\) If \(k=-3\) (greatest negative integer) \(\Rightarrow(-i)^{-3}=-i\) So, \(m=1\) and…
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