JEE Mains · Maths · STD 11 - 4.1 complex nubers
The least positive integer \(\mathrm{n}\) such that \(\frac{(2 \mathrm{i})^{\mathrm{n}}}{(1-\mathrm{i})^{\mathrm{n}-2}}, \mathrm{i}=\sqrt{-1}\) is a positive integer, is ..... .
- A \(2\)
- B \(4\)
- C \(6\)
- D \(8\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
\(\frac{(2 \mathrm{i})^{\mathrm{n}}}{(1-\mathrm{i})^{\mathrm{n}-2}}=\frac{(2 \mathrm{i})^{\mathrm{n}}}{(-2 \mathrm{i})^{\frac{\mathrm{n}-2}{2}}}\)…
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