TS EAMCET · Maths · Complex Number
If \(n\) is a positive integer, then \((1+i)^n \div(1-i)^n=-i\), then \(n\) will be of the form
- A \(4 k-3, k \in N\)
- B \(4 k-1, k \in N\)
- C \(4 k-2, k \in N\)
- D \(4 k, k \in N\)
Answer & Solution
Correct Answer
(B) \(4 k-1, k \in N\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, } \frac{(1+i)^n}{(1-i)^n}=-i \\ & \Rightarrow \quad\left(\frac{1+i}{1-i}\right)^n=-i \\ & \Rightarrow \quad\left[\frac{(1+i)(1+i)}{(1-i)(1+i)}\right]^n=-i \\ & \Rightarrow \quad\left[\frac{(1+i)^2}{1+1}\right]^n=-i \\ & \Rightarrow…
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