Complex Numbers
Powers and De Moivre's Theorem
JEE Main
Grade 11
Question:
The least positive integer $n$ for which $\left(\frac{1 + i}{1 - i}\right)^n = 1$ is:
(1) $2$
(2) $4$
(3) $6$
(4) $8$
Step-by-Step Solution
Key Concept: Simplify $(1 + i)/(1 - i)$ by rationalising. Identify the result as a power of $i$, then find the smallest $n$ for which that power equals $1$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)