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)

${\left(\begin{array}{c}\frac{1+i\sqrt{3}}{1-i\sqrt{3}}\end{array}\right)}^n=1$
${\left(\begin{array}{c}\frac{-2{\omega }^2}{-2\omega }\end{array}\right)}^n=1$
${\omega }^n=1$
least positive integer value of n is 3.