Question

The least positive integer n for which $\left( \frac{1 + i \sqrt{3}}{1 - i \sqrt{3}} \right)^n = 1$, is :

• A. 2
• B. 3
• C. 5
• D. 6

Answer 1

Answer: (B)

3

Answer 2

$\begin{pmatrix}\frac{1+i\sqrt{3}}{1-i\sqrt{3}}\end{pmatrix}^{n} = 1$ $\begin{pmatrix}\frac{-2\omega^{2}}{-2\omega}\end{pmatrix}^{n} = 1$ $\omega^{n} = 1$ least positive integer value of n is 3.